Preheat the broiler. Heat the vegetable oil in a large nonstick skillet over medium heat. Add the bacon and cook, turning occasionally, until browned, about 10 minutes. Transfer to a paper towel?lined plate to drain, then crumble into small pieces.
Split the whole pack of attached dinner rolls in half horizontally. Place the top and bottom halves cut-side up on a baking sheet. Brush with all but 1 tablespoon of the melted butter and broil until toasted, 1 to 3 minutes. Remove the top bread piece from the baking sheet. Flip the bottom piece and continue to broil until toasted on the other side, 1 to 2 more minutes. Remove from the oven and preheat to 400 degrees F.
Turn the bottom bread piece cut-side up and sprinkle with the bacon. Top with the chopped tomato, then shingle the provolone and muenster on top, alternating the two. Cover with the top bread piece, then brush the roll tops with the remaining 1 tablespoon melted butter. Bake until the bread is toasted and the cheese is melted, 12 to 15 minutes.