Place 1 cup roasted red peppers and 8 jalapeño slices on a cutting board; finely chop together into a rough paste. Transfer the mixture to a small bowl. Add chopped basil, 3 tablespoons oil, 2 teaspoons vinegar and ⅛ teaspoon salt; stir until well combined.
Spread about 2 tablespoons of the pepper mixture over each ciabatta slice; top each with ½ cup shredded lettuce and 2 tomato slices. Divide sliced avocado and the burrata pieces among the sandwiches; drizzle with the remaining pepper mixture. Serve immediately.
