Cecily Strong, whose hilarious invention of logorrheic self-ignorance, “The Girl You Wish You Hadn’t Started a Conversation with at a Party,” has made her a breakout star of Saturday Night Live, met me for lunch at Trattoria Dell’Arte, opposite Carnegie Hall in Midtown Manhattan, close to where she lives.

It became clear from the start that the vivacious Ms. Strong cannot be anticipated in anything she says. We had scarcely met when mention of pasta compelled her to confide with transparent candor, “I was just in Rome. I’m having an Italian love affair. I first met him in Seville, Spain, before I broke my foot in Ibiza.”

“What does the lucky guy do?”

“He’s studying to be a diplomat, which is nice. It’s all very new. So who knows if it’ll be a thing? But it’s still fun. He reminds me of Roberto Benigni in a way. We’ve talked every day for two months. I’m not rushing into anything, I promise. If I were too emotionally attached, I’d be too scared to talk about it.”

She’s a naturally funny woman—particularly when she’s serious. She can’t help herself. Could she remember the first time she made anyone laugh? “When I sang ‘Rudolph the Red-Nosed Reindeer’ to my parents in a French accent,” she replied. “It was very lounge-y. I think I did a little lounge dance.”

Born in 1984, she was raised in Oak Park, Illinois. Her parents sent the precocious three-year-old Cecily to a local pre-school drama class. “There were only three of us in the class—another little girl and boy. I did not like that little boy. We were supposed to do The Frog Prince, and he was the prince and I was the princess. But I threw a fit because I didn’t want to do it with him, and so we wound up doing The Elves and the Shoemaker instead. I went from a princess to an elf—and it felt much more comfortable. That’s how I should have known I was going to end up in comedy. I cried about being a princess. And I was like, Yes! I’m an elf!”

She scanned the menu and declared, “I love stuffed baby artichokes.” (She doesn’t eat meat.) We shared a feast of the vegetable antipasti—the artichokes, Sicilian eggplant caponata, stuffed peppers, broccoli rabe, hen-of-the-woods mushrooms, and, for good measure, green beans with quinoa. (“Love green beans.”) Drink? “I’ve got to stay awake today. I wish I could, but not yet. If it were later.” She settled for an iced tea.

Cecily’s route to Saturday Night Live came via her time as an understudy at Chicago’s phenomenal mecca of improvisatory comedy, Second City. (Among its renowned alumni: Gilda Radner, John Belushi, Bill Murray, Dan Aykroyd, Steve Carell, Tina Fey, Stephen Colbert.) It takes a scary kind of courage to improvise comedy. “There was a long time in Chicago when I kept thinking, Am I like one of those people on American Idol who doesn’t know they’re not good?”

She persevered, regardless of her innate anxiety and fears, and supported herself with several jobs, including performing on a cruise ship with fellow Second City members for four months. “It was half vacation, half prison.” What were the audiences like? “It depends on where you’re porting. I only knew the fun people who came from New York and New Jersey. I think a lot of people in their twilight years die on cruises. Cruise ships have mortuaries. That was the rumor, anyway. I think we had a couple of people pass away on our ship.”