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They grow up so fast.

Brooklyn’s obsessive coffee culture is rubbing off on the borough’s youngest cafe-goers, with tots ditching their bottles and juice boxes in favor of “babyccinos” — mini decaf cappuccinos or frothy cups of steamed milk and foam.

Moms and dads in neighborhoods like Park Slope, Fort Greene and Prospect Heights are ordering the small, foamy, surprisingly grown-up beverages for their pint-sized offspring.

And the kids are asking for refills.

“Our children love babyccinos!” said Eric Worcester, who ordered the milk-only variety for his kids, Evelyn, 5, and Shirley, 2, at Sit and Wonder on Washington Avenue on Saturday (He and his wife had more traditional beverages).

The folks behind Sit and Wonder also sell babyccinos at their Fort Greene coffeehouse Bittersweet, where a barista said she serves up between five and 10 of the kiddie drinks daily.

Gemma Redwood, co-owner of the two coffee joints, made sure her cafes were child-friendly by outfitting Sit and Wonder with a changing station in the bathroom and a backyard filled with toys. But she only started selling a $2 coffee-free variety of the drink —which is not officially on the menu — due to popular demand.

“I think it was from a TV show or something,” said Redwood, who does not allow her two young children to sip the faux-adult beverages. “It’s a little weird — but we make it.”

Baristas at many other coffeehouses around the borough such as Cafe Regular in Park Slope and Root Hill Cafe in Gowanus admit they make the baby drinks. But babyccinos had some coffee-sellers — who are frequently frustrated by requests for highly specific off-the-menu items — drawing a line in the foam.

“I have one customer who says that and it annoys the hell out of me,” said Sean Chin of Gorilla Coffee in Park Slope. “It is not on our menu — which we are making an effort to stick to.”

Babyccino is hardly a scientific term, with some shops and customers using the word to describe a macchiato-like beverage featuring a shot of decaf espresso topped with steamed milk and froth, while others use it to describe steamed milk with foam on top and a touch of cinnamon. Baristas around the borough say they get requests for both versions of the drink.

The trend started in Australia about a decade ago with milk-only babyccinos and quickly became the bane of many a barista’s existence, according to Aussie coffee expert Paul Caligiore.

“They interrupt workflow, create milk wastage and can be served at a dangerous temperature to a vulnerable consumer,” said Caligiore, who despite his misgivings about the drink plans to begin selling the world’s first instant babyccino. “Babyccinos have become so popular in Australia it would be difficult to find a cafe that doesn’t have them on their menu.

The trend spread to England and the internet, with YouTube serving as a popular repository of videos of parents making the beverage for their kids.

Fans of babyccinos say the drink’s popularity has surged in Brooklyn over the last few months.

The concoction might be Brooklyn’s first coffee beverage marketed primarily to children, but it’s certainly not the first time the borough’s adult venues have catered to kids.

The Tea Lounge in Park Slope offers “stroller parking” and makes a point of allowing patrons to breastfeed their infants on the cafe’s many couches. Der Schwarze Kolner, a beer garden in Fort Greene, hosts a weekly playgroup for parents and their toddlers.

Babyccinos can help coffee shops reach a whole new generation of java drinkers — and that’s not necessarily a bad thing for children, so long as they stick to decaf.

Doctors say that caffeine is not healthy for kids in large quantities, but a decaf shot of espresso contains less caffeine than a soda.

“A small percentage of caffeine on a non-regular basis is probably okay,” said Dr. Deena Blanchard, a pediatrician at Premier Pediatrics who remained skeptical of the kiddie coffee.

Lots of Brooklyn moms have no qualms exposing their kids to the borough’s booming cafe culture.

“My child has been going to cafes since he was a newborn,” said Katherine Haver, a freelancer who works out of coffee shops, sometimes with her nearly two-year-old son. “ ‘Coffee shop’ was one of his first words.”

Reach reporter Eli Rosenberg at erosenberg@cnglocal.com or by calling (718) 260-2531. And follow him at twitter.com/emrosenberg.