Elana Carlson, who grew up in a Jewish family in Sudbury, was brainstorming names for her burgeoning bagel business when suddenly it hit her.

“My grandma spoke Yiddish a lot when I was younger,” Ms. Carlson said on a recent Friday morning, seated at a picnic table outside Kitchen Porch Catering where she bakes her sourdough delicacies each week. “We were just playing around with words and gibberish and came up with fancy...and the word just stuck.”

Inspired by her grandmother, Ms. Carlson found the Yiddish word for fancy, trimmed a letter, funkified it, and Fantzye Bagels was born.

Bagles are pre-ordered and picked up Sundays at State Road Restaurant from 9:30 a.m. to noon. — Ray Ewing

Ms. Carlson, who has been baking bagels for small crowds and weekend pop-ups across the Island since last spring, is launching her business officially this summer, with plans to host weekly bagel pickups on Sundays at State Road throughout the season. Starting this weekend, customers can pre-order the Brooklyn-style sourdough bagels with cream cheese and toppings for pickup between 9:30 a.m. and noon.

Ms. Carlson earned her culinary stripes managing restaurants and staging in kitchens like Mission Chinese in New York city. In 2014 she moved to the Vineyard to work at the Beach Plum Inn, and the next summer managed the food and natural wine program at Behind the Bookstore. She relocated to Los Angles for a few years but returned to the Vineyard last May. The idea for bagels came soon after, inspired by a pop-up she co-hosted at Seaweed’s Restaurant last July.

“We did the [pop-up] and it was super successful, we sold out in a second,” Ms. Carlson said. “I remember thinking, there’s something here.”

Enlisting the help of her two roommates and fellow culinary professionals, Nina Krane and Gina Citarella, Ms. Carlson began experimenting with sourdough bagel recipes, using the oven at Kitchen Porch Catering. More pop-up events followed throughout the fall.

Elana Carlson looks to expand the business as the season unfolds. — Ray Ewing

The Fantzye menu, which rotates seasonally, is built around airy sourdough bagels, cooked on handmade bagel boards to achieve a classic New York-style bagel with a tangy twist, Ms. Carlson said.

Accompanying the bagels is an ever-changing list of cream cheeses and pickled vegetable options, featuring ingredients sourced from local farms. Among her favorite offerings have been beet and horseradish cream cheese, roasted leek spread and lacto-fermented chili schmear.

“It’s like a very thought-out composition of things that you can assemble as you want...like a choose your own adventure,” she said.

Ms. Carlson cited chefs Alice Waters and Ignacio Mattos as influences, as well as small bagel shop owners across the country.

“There is kind of a bagel boom happening right now across the country. A really fun part of this has been talking to other small bagel makers...in Maine and California and all over and building on the boom.

Ms. Carlson recently added a second bagel pick-up the last Friday of each month, beginning May 28, at Vintage MV Wine and Spirits in Edgartown.

Along with bagels, Ms. Carlson is planning to cook weekly dinners on Mondays at State Road, featuring a prix-fix menu of seasonal, bistro-style fare and natural wine consultation. The first Fantzye Supper will be held on Memorial Day. A handful of other collaborations with local businesses, including a wine club, are also on the horizon for later in the season.

Looking ahead, Ms. Carlson said she hoped to establish a more permanent brick-and-mortar shop one day. But for the moment, the joy is in the cooking, she said.

“We’re just really excited to be doing our own thing. We just want to cook good food for people and not take it too seriously.”