Cook bacon in a large, deep skillet over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain on a paper towel-lined plate.

Mash black-eyed peas in a bowl with a fork. Crumble bacon into the bowl, then stir in red peppers and shallot. Stir in enough flour to make the mixture stick together. Season with salt and pepper and form into four equal patties.

Heat butter and oil in a large skillet over medium heat until butter melts. Add patties and cook until golden brown and crispy, about 4 minutes per side.