Melt butter and olive oil in a large skillet over medium heat (5 out of 10.) Add onions and toss to coat. Cook for 25-30 minutes, stirring occasionally, until onions are soft and golden brown. Turn heat down during the cooking process if onions begin to burn. Meanwhile, cut fontina cheese into 8 cubes. In a large bowl, combine ground beef with onion soup & dip mix and water, then form into 8 balls. Push your thumb into the balls to create an indentation, then stuff with a cheese cube. Seal tightly, then flatten slightly into a patty. Repeat with remaining cheese and ground beef. Heat grill to medium-high, then grill sliders for 5-6 minutes a side. Remove to a plate, cover with foil, then let rest for 5 minutes. Toast buns briefly on the grill, then top sliders with caramelized onions and serve.