Melt butter in a skillet over medium heat; stir in banana peppers, chile peppers, tomato, and onion. Cook and stir until the onion has softened and turned translucent, about 5 minutes. Add cooked beef, salt, and pepper; stir until heated through, about 1 minute.

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Whisk eggs together in a bowl. Pour into the skillet with the vegetable mixture; cook and stir until eggs are set, about 5 minutes.

Meanwhile, warm tortillas, one at a time, in a dry skillet over low heat.

Place a medium scoop of the egg mixture on each tortilla. Add cheese and roll up, leaving one end open. Add a small dollop of sour cream to each bite, if desired.