Broil bell peppers on a broiler pan 5 inches from heat, turning occasionally, until skins are blackened, about 15 minutes. Transfer to a bowl and let stand, covered, until cooled slightly, 10 minutes. Peel peppers, discarding stems, then cut lengthwise into 1/4-inch strips.
Whisk together eggs, milk, cheese, garlic, salt, and black pepper in a large bowl, then stir in tomatoes and basil.
Heat 2 tablespoons oil in a 12-inch nonstick skillet over moderately high heat until hot but not smoking. Pour in egg mixture and cook, lifting up cooked egg around edge occasionally to let raw egg flow underneath, 3 minutes. Reduce heat to low and cook, covered, until underside is golden, about 5 minutes more. Slide onto a plate, then arrange bell peppers over top in a wheel-spoke pattern.
Invert skillet over plate and (wearing oven mitts) flip frittata over into skillet. Drizzle remaining oil around edge of frittata and shake to help distribute underneath. Cook, covered, over moderately low heat until underside is golden and frittata is cooked through, about 5 minutes. Invert a large clean plate over skillet and (wearing oven mitts) flip frittata onto plate. Sprinkle with parsley and cut into 6 wedges.
Cooks' note: To peel tomatoes, first cut an X in the end opposite the stem, then immerse in boiling water 10 to 15 seconds. Transfer to a bowl of ice and cold water, then peel.