Add the (drained) butter beans, lemon zest, lemon juice, garlic, salt, pepper, and chili flakes to a food processor and puree until relatively smooth (about 2-3 minutes). Add 1 tablespoon of extra-virgin olive oil and puree for another 30 seconds to blend the oil in.
Toast the bread slices (either in the toaster or in a skillet). Toasting them in the skillet will make them more indulgent as we’re brushing them with olive oil. If toasting them in a skillet, brush them with olive oil (about two tablespoons total for all four slices) and toast them in a skillet, cast iron pan, or grill pan for about 2 minutes on each side over medium-high heat until golden-brown.
Assemble the ingredients: the toasted bread, the seasoned mashed beans, the pesto, and the burrata.
Spread the pureed beans on the toasted bread. Add 1/4 of the burrata to each of the bread slices, on top of the mashed beans. Drizzle about 1 tbsp of pesto over each slice.