Cook ground beef in a large nonstick skillet over medium-high heat, stirring until it crumbles and is no longer pink.
Remove from skillet, and drain well. Wipe skillet clean with a paper towel.
Melt butter in skillet over medium-high heat.
Add bell pepper strips and sliced mushrooms, and saut 8 minutes or until mushrooms are lightly browned and liquid evaporates.
Remove from heat; stir in beef, 1 jar pizza sauce, and cheese.
Unroll each can of pizza crust dough on a lightly floured surface; cut each crust into quarters. Press each dough quarter into a 7- x 6-inch rectangle. Spoon about 2/3 cup meat mixture in the center of each rectangle. Fold 1 short side of dough over filling, pressing or crimping edges to seal.
Place beef pockets on 2 lightly greased baking sheets, and cut slits in tops to allow steam to escape.
Brush lightly with olive oil.
Bake, on separate oven racks, at 375 for 25 to 30 minutes or until golden. (Switch places of baking sheets in oven after 15 minutes if necessary for even baking.)
