Slice roast in half horizontally; sprinkle with salt and pepper. In a skillet over low heat, cook roast and two garlic cloves in 3 tablespoons oil for 20 minutes, turning to brown all sides.
Meanwhile, in another skillet, cook spinach and mushrooms in remaining oil for 3-4 minutes or until tender. Add remaining garlic; cook 1 minute longer. Drain well. Remove from the heat; stir in cheese.
Place breadsticks 1/2 in. apart in a greased 15x10x1-in. baking pan, stretching dough slightly so each breadstick is about 13 in. long. Lay one roast half in the center of the dough. Spread spinach filling evenly over roast. Top with other half of roast. Bring ends of a breadstick to the top of the roast, twisting and pinching to seal. Repeat with each breadstick.
Bake at 350° for 20-35 minutes or until thermometer reads 145°. Let stand for 10 minutes before slicing.