In a large skillet, heat 2 tablespoons of vegetable oil over medium heat. Add the diced onions and cook for 4-5 minutes until softened and translucent. Add minced garlic and cook for another minute until fragrant.

Add the diced tomatoes to the skillet along with tomato paste, stirring to combine. Cook for 3-4 minutes until the tomatoes begin to break down. Add chili powder, cumin, paprika, oregano, and cayenne pepper. Stir well to incorporate all spices.

Add the shredded chicken thighs to the tomato mixture. Stir to coat the chicken thoroughly with the sauce. Add chicken broth and let the mixture simmer for 15-20 minutes, stirring occasionally, until the liquid reduces and the tinga reaches a moist but not soupy consistency. Season with salt and black pepper to taste.

While the tinga simmers, heat 1/2 inch of vegetable oil in a separate large skillet over medium-high heat. Once the oil reaches 350°F, carefully add tortillas one at a time and fry for about 45-60 seconds per side until golden and crispy. Remove to a paper towel-lined plate to drain excess oil.

To assemble the tostadas, place each crispy tortilla on a serving plate. Spread a generous layer of tinga de pollo on top. Add a layer of shredded lettuce, then drizzle with sour cream. Sprinkle with crumbled cheese and garnish with fresh cilantro. Serve immediately while the tostadas are still crispy.