Combine onions, butter, olive oil, salt, and pepper in a slow cooker. Set to HIGH for six hours. Stir once after a few hours. 

Add two cups of vegetable stock and cook on high for another hour. Meanwhile, preheat oven to 400 degrees.

Slice each roll lengthwise and place open-faced on a baking sheet. Divide cheese evenly, covering both sides of each roll. 

Using a slotted spoon, scoop onions out of the slow cooker and squeeze out excess liquid by pressing another spoon on top of the slotted one. Pile onions onto the bottom half of each roll.

Bake for 5-10 minutes until cheese is bubbly and the bread is golden. Ladle onion broth into small bowls and serve with sandwiches for dipping.