Preheat the oven to 350°.Brush each side of the tortillaswith 1/4 tsp. oil. Bake directly on oven racks until crispy, 15 to 18 minutes. Let cool.
In a food processor, puree 2 cups lettuce tops with the mayo, garlic and Serrano chiles; season the sauce with salt.
Preheat a large cast-iron skillet over high. In a large bowl, toss the poblanos, zucchini and shrimp with the remaining 4 tsp.oil and the cumin; season with salt and pepper. Cook, turning occasionally, until the shrimp is cooked through, 4 minutes. Transfer the shrimp to a plate and continue cooking the chiles and zucchini until blackened in spots, about another 4 minutes. Cut the zucchini and poblano strips crosswise into thirds.
Form tostadas with tortillas, remaining lettuce, poblanos, zucchini and shrimp. Drizzle with some sauce; top with cheese. Pass remaining sauce.