Pour the vegetable oil into a medium nonstick skillet over medium-high heat. Add 1 or 2 tortillas at a time, depending on the size of your skillet, and toast in the hot oil until both sides are crispy, 3 to 4 minutes for each. Transfer to a plate lined with paper towels.
Heat the refried beans in a small saucepan over medium heat until warmed through.
To assemble each tostada, begin with a layer of 1/4 cup refried beans over each crispy tortilla. Top with about 1/4 cup of the cheese, followed by the same of the chicken, cabbage, tomatoes and avocado. Finish each tostada with a generous squeeze of lime juice and season with salt and pepper. If desired, serve with your favorite salsa.
Baby version: Rather than an open-faced tostada, make a kid-friendly quesadilla that's easier to eat for your little one. Begin assembling by layering 1/4 cup refried beans over 1 corn tortilla (not toasted. Follow the same assembly directions as listed above with the exception of the cabbage. Top the layers with an additional corn tortilla and cook in a non-stick skillet with a glug of vegetable oil over medium-high heat. Flip quesadilla occasionally until cheese is melted. Cut into bite size pieces before serving.