Preheat oven to 400 degrees. On a rimmed baking sheet, toss tortillas with 1 tablespoon oil; season with salt. Toast in oven until golden brown, tossing occasionally, 15 to 20 minutes.
Meanwhile, in a small saucepan, warm remaining tablespoon oil over medium heat. Add onion, jalapenos, and garlic; season with salt and pepper. Cook, stirring, until onion is translucent, about 5 minutes. Add chicken broth, and bring to a boil; reduce heat, and simmer 5 minutes. Transfer to a blender; puree until smooth.
Spread toasted tortilla strips on an ovenproof platter or in a baking dish; scatter cheese and turkey over strips. Bake until cheese has melted, 3 to 4 minutes. Remove from oven; drizzle chile puree over the top. Serve immediately.
Note: When blending hot liquids, keep the large rubber cap on the blender, but remove the small plastic air-hole cover; hold a dish towel over the hole to vent the heat and prevent the liquid from spilling out.