“I love the sweet aroma of squirrel, and I’m surprised at most folks’ inexperience with serving the little guys,” says chef Levon Wallace, who heads up the kitchen at Proof on Main in Louisville, Ky.

As the kitchen manager at the Odd Soul, a pizzeria and bar in Springdale, Arkansas, Addie Hayes is used to spending Saturday mornings in front of a stove. But today, she’s a little out of her element.

If New Year’s resolutions include spending more time outdoors, keep your eyes and ears open for red squirrels. They’re sporting their brightest, thickest fur this time of year and ready to pitch a fit ...