Preheat a panini grill (if you have one) or a nonstick griddle. Or if you have a large cast-iron skillet, that works well too. (For anything on the stovetop, preheat the pan over medium-high heat.)
In a small bowl, combine the two cheeses. Lay out the 8 slices of bread on a cutting board and brush one side of each with olive oil. Flip them over (oil-side down) and top 4 slices with 1/4 cup cheese. Top each with a slice of bread, oil-side up.
Working in batches, cook the sandwiches on the panini grill (or griddle or cast-iron skillet) until they are golden brown on both sides and the cheese is oozing out. If you use a cast-iron skillet, place another pan on top of the sandwiches while they’re cooking, to get a nice crispy exterior.
Cut the sandwiches in half, and serve with roasted tomato basil soup (recipe above).
NOTE: Feel free to swap out cheeses as you please: you could try just cheddar or just Gruyere, or Asiago, mozzarella, Brie, or really anything you please! I just happen to love the combo of sharp cheddar and nutty Gruyere.