Cut half of onion into 3/4-inch wedges, then chop remainder. Toss onion wedges, tomatoes, garlic, and whole chiles with 2 tablespoons oil in a 4-sided sheet pan, spreading in 1 layer.
Broil about 4 inches from heat until softened and charred, 10 to 15 minutes. Meanwhile, toss together lettuce, radishes, chopped onion, and half of cilantro.
Purée tomato mixture in a blender along with one or both roasted serranos (to taste) and 1 teaspoon salt until smooth (use caution when blending hot foods). Transfer purée to a bowl and stir in chicken, remaining cilantro, and salt to taste.
Heat remaining 1/2 cup oil in a heavy medium skillet over medium-high heat until it shimmers. Fry tortillas, 1 at a time, turning once or twice and pressing with tongs to immerse, until golden brown, 45 to 60 seconds per tortilla. Drain briefly on paper towels, then transfer to plates.
Spread tortillas thickly with heated refried beans, then top with chicken mixture. Slice avocado over tostadas and dollop with crema.
Mound lettuce mixture on top and sprinkle with cheese.