In a bowl, mix together the cooked ground beef, rice, and salsa until well combined.
Place a tortilla on a clean surface and sprinkle ½ cup of shredded cheese in the center.
Add about ½ cup of the ground beef and rice mixture on top of the cheese.
Fold the sides of the tortilla over the filling, then roll from the bottom to enclose the mixture, forming a burrito. Repeat with the remaining tortillas and fillings.
Heat a large skillet over medium heat and add ½ tablespoon of butter.
Once the butter is melted and bubbly, place a burrito seam-side down in the skillet. Grill for about 3-4 minutes on each side, until the tortillas are golden brown and crispy, and the cheese is melted.
Remove from the skillet, and place on a cutting board. Allow to cool for a minute, then slice in half diagonally.
Serve warm with sour cream on the side for dipping, if desired.