Mix Dry Ingredients Combine flour, yeast, salt, and cinnamon in the bowl of a stand mixer fitted with a dough hook attachment; beat on low speed until combined, about 1 minute.

Mix Dough Process carrots, milk, egg, and 2 tablespoons of the honey in a blender until smooth, about 1 minute. Add carrot mixture to stand mixer bowl; beat on low speed until a soft, tacky dough forms, about 2 minutes. With mixer still running on low speed, add 2 tablespoons of the butter, and beat until butter is completely incorporated, 1 to 2 minutes. Increase speed to medium; beat until dough is smooth and elastic, but still tacky to the touch, 8 to 10 minutes. If necessary, add more flour, 1 tablespoon at a time, until mixture is slightly sticky, up to ¼ cup total.

Let Rise Transfer dough to a medium bowl coated with cooking spray. Cover with plastic wrap and let rise in a warm place (about 85°F) until doubled in size, 30 minutes to 1 hour.

Prep Pan Preheat oven to 350°F. Spray a 13- x 9-inch baking pan with cooking spray.

Form Rolls Turn dough out onto a lightly floured work surface. Punch dough down and divide into 15 equal pieces (about 2 ounces each); roll each piece into a ball. Place balls in prepared pan. Cover pan with plastic wrap, and let rise in a warm place until doubled in size and dough springs back slowly when gently pressed, 50 minutes to 1 ½ hours.

Make Honey Butter Meanwhile, stir together remaining 1 tablespoon honey and 1 tablespoon butter; set aside.

Bake and Serve Uncover rolls, and bake in preheated oven until golden brown, about 20 minutes. Brush hot rolls with honey butter; sprinkle with flaky sea salt. Serve immediately, or transfer rolls to a wire rack to cool completely, about 30 minutes.