Position a rack in the center of the oven and heat the oven to 350°F. Generously coat a 24-cup mini muffin pan with cooking spray.
Melt the butter in a heavy-duty 1-quart saucepan over medium heat. Cook, swirling the pan occasionally, until the butter turns a nutty golden-brown, about 4 minutes. Pour into a small bowl and let cool.
In a medium bowl, combine the flour, polenta, Cheddar, baking powder, 1 tsp. salt, and a few grinds of pepper.
In a stand mixer fitted with the whisk attachment, beat the eggs and sugar on medium speed until pale yellow and thickened, 3 to 4 minutes. Reduce the speed to low. Add a third of the dry ingredients, then half of the melted butter, mixing after each addition until just incorporated. Alternately add the remaining flour and butter, mixing after each addition, and ending with the dry ingredients. Stir in the roasted red peppers and scallions by hand.
Spoon the batter into the prepared muffin pan (about 1 Tbs. per muffin). Bake until a toothpick inserted into the center of a muffin comes out clean, 10 to 15 minutes.
Let cool on a wire rack for 15 minutes and then unmold. Serve warm.
The muffins may be baked up to 8 hours in advance. To reheat, wrap in foil and heat in a 350°F oven until warm, 7 to 10 minutes.