Heat olive oil in a large skillet over medium high heat. Add shrimp, season with salt and pepper to taste; cook for 4-5 minutes, stirring and flipping occasionally, until the shrimp are pink and cooked through. Stir in the chimichurri sauce, and toss until the shrimp are evenly coated. Turn off the heat and set aside.
Cut 12 mini round tortillas with 3-inch round cutter (if desired, stack 2 or3 tortillas to cut).
Heat the oil for frying into a large skillet (about 2 inches in depth) to 375ºF. Add the tortillas, one at a time, and fry until golden brown and crispy, about 1 1/2 minutes. Using tongs, transfer to a paper towel-lined pan and sprinkle with salt. Set aside.
To serve, divide the shrimp mixture between the mini tostadas. Top each with avocado and sprinkle with queso fresco and cilantro leaves.
Serve with lime wedges, if desired.