Beneath the live oaks at the bottom of Griffith Park, there’s a dark-wooded, old-school snack shack that feels like it’s been plucked out of a ‘70s Adirondacks resort. We’ve been hiking for a good 90 minutes with only a bottle of water, and Kroll makes a beeline for the ordering window, where two teenage girls are harvesting their tips from a Mason jar. Kroll scans the menu and starts chanting, “Y’all got that pie, gotta have that pieeeeeee.”

Kroll stuffs a $5 bill into the jar and scans the surrounding picnic tables, half of which are occupied with hikers in various states of occupied conversation. Kroll bypasses a few obvious choices, pauses, scans again, and apologizes: He’s just trying to find the place farthest from everyone else. No one’s recognized him or approached him yet, but he’s still wary of being overheard.

Most dudes of a certain age, especially the type of dude whose media diet consists mostly of sports and Comedy Central, know exactly who he is. But his stardom remains niche: He’s less famous than many of the reality-star characters he indirectly lampoons.

Kroll is conflicted about this. When I call him a “demi-star,” he chuckles and asks, “Is that what I am?”

"It's constant combinations of things,” he explains, forking the enormous slice of pie — vegan strawberry-rhubarb, with a heaping scoop of vanilla ice cream. We discuss an academic theory of stardom — that to be an Angelina Jolie/Brad Pitt/Reese Witherspoon type of star, you have to have a “textual” persona (the way your characters all seem on-screen) and an “extra-textual” (real life) one that seem to complement each other. Celebrity analysis comes easily to Kroll, even as he insists, “I don’t particularly like talking about other people’s careers.” We set off on trip two into the park as a busload of teen girls rolls by.

“Take Chris Pratt versus Michael Cera,” Kroll riffs. “Michael Cera was, like, the nerd king of 2008; he could be the star of any movie he wanted, and he dips out and quote-unquote makes the wrong choices, or nerd culture doesn't actually translate that easily into who [people] want as their central protagonist, and then you've got Chris Pratt, who's like a hulking American man, who's sweet and funny and charming." As Kroll continues, “You could argue that some version of that is that Cera, at the end of the Bush administration, is someone you want to root for, this little hipster; whereas now, coming to the end of the Obama administration, everyone's thirsty for a red-blooded American male."

Could we ever be thirsty for Kroll? Would Kroll ever want us to be? The closest he has to a textual persona is Ruxin on The League, but his Kroll characters disassemble any sense of coherency. And all those seem a far cry from Kroll’s real-life image, at least as gleaned through Poehler’s description: “I have a boyfriend who knows how to settle me,” she writes in Yes Please. “He puts his hand on my chest and tells me boring stories. On one of our first nights together I woke up apologizing for my snoring and he pulled out his two earplugs he had worn to bed so he could hear what I was saying. It was one of the most romantic gestures I have ever seen.”

But that incoherency is part of Kroll’s implicit goal. Unlike a comic like Louis CK, “I’ve ended up doing a lot of characters partly because I’m like, what level do I want to talk about my personal life? I won’t share everything, both in my act or in interviews. Some of the people who become the most famous are the most self-revelatory, and I’m like, no, it’s just not worth it to me.”

By the time we make it back down from the second trip up the hill, Kroll is hungry or antsy or both, so we get back in his Subaru and drive into Los Feliz. The conversation winds toward a recent trip to Mexico “with my family and girlfriend,” after which he took four days to go to Mexico City on his own.

“I was like, I just want to go remember what it was like to be on my own and also — this sounds cheesy — not at all famous.” So he arrived in Mexico City, where he serendipitously ran into a woman who once lived down the street from him. “I was glad because we hung out and went to museums together,” Kroll says. “I ended up hating being alone-alone. I was reading The Goldfinch, and it's about an orphan, alone in the world, and I had a very visceral experience. I was in a cold, rainy, largely outdoor hotel with nothing to do, and reading my book alone at dinner, and I was like, I feel it."