Preheat the oven to 425°F (220°C). Zest the limes to yield 1/2 teaspoon zest and juice them to yield 5 tablespoons lime juice; set aside. Warm the pinto beans if using homemade or canned.
Make the cilantro-cashew sauce: place the cashews in a heatproof bowl and pour 1 cup boiling water over them. Let soak 45–60 minutes, then drain thoroughly.
In a high-powered blender, combine the drained cashews, cilantro, 3 tablespoons lime juice, lime zest, 1/3 cup water, olive oil, 1/2 teaspoon garlic powder, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Blend until completely smooth, then refrigerate.
Prepare the avocado topping: scoop the avocado flesh into a medium bowl and mash with a fork. Stir in 2 tablespoons lime juice, 1/4 teaspoon salt, 1/8 teaspoon pepper, and 1/8 teaspoon garlic powder until combined.
Arrange the tortillas on a sheet pan without overlapping. Spray both sides lightly with cooking spray and sprinkle both sides with a pinch of salt. Bake 4 minutes, flip with tongs, then bake another 3–6 minutes until crispy. Let cool 5–10 minutes.
Assemble the tostadas: spread about 1/4 cup beans on each crispy tortilla, then divide the mashed avocado among the 6 tostadas. Top with shredded lettuce, halved cherry tomatoes, and sprinkle with queso fresco.
Drizzle the chilled cilantro-cashew sauce over the tostadas to taste and serve immediately.