Mash half of peas in a bowl with a fork and stir in remaining peas. Cook red peppers in butter in a large nonstick skillet over moderate heat, stirring, until barely softened. Add garlic and cook, stirring, 1 minute more. Transfer 1/3 of pepper mixture to a bowl and cool. Set aside for red pepper mayo.
Stir remaining pepper mixture into peas with bread crumbs, cilantro, eggs, cumin, and salt. Scoop 1 tablespoon mixture into palm of your hand (mixture will be soft and moist) and form into a roughly 1-inch-wide patty. Put it on a tray and form more patties in same manner, arranging in 1 layer on tray. Dip patties, 1 at a time, into cornmeal, turning gently to coat, and transfer as coated to a tray lined with waxed paper and dusted with cornmeal. Chill patties, covered, at least 2 hours and up to 8.
Preheat oven to 400 degrees. Heat 3 tablespoons oil in a 12-inch nonstick skillet over moderate heat until hot but not smoking, then cook cakes, 12 at a time, until golden, about 3 minutes on each side. Put cakes as cooked in 1 layer in a large shallow baking pan. Between batches, carefully wipe skillet clean with paper towels and add more oil. Stir mayonnaise into reserved red pepper mixture and season with salt and pepper. Reheat cakes in middle of oven until hot, about 5 minutes, and top with red pepper mayo.