Melt butter in a skillet over medium heat. Cook and stir bell pepper and onion in hot butter until onion is translucent and pepper is tender, about 5 minutes. Add beef; cook and stir until the beef is hot, about 5 minutes more. Remove from heat.

Pour enough canola oil into a saucepan to reach about 1 inch deep; heat to 375 degrees F (190 degrees C).

Arrange tortillas on a flat surface; place halves of cheese slices end to end lengthwise onto each tortilla. Layer an equal amount of steak mixture atop each cheese slice. Roll tortilla around filling as you would a burrito, with the sides tucked in to close the ends, forming chimichangas.

Cook chimichangas in the hot oil until browned completely, about 5 minutes per side; drain on paper towels.