Preheat the oven to 350°F (175°C).
Prepare the garlic: trim the top off both garlic bulbs to expose the cloves, remove any loose papery outer layers, place the bulbs on a sheet of foil, drizzle the exposed cloves with the 1 teaspoon olive oil, and wrap each bulb tightly in the foil.
Roast the wrapped garlic bulbs on a baking sheet for about 1 hour, until the cloves are golden and caramelized. Let the bulbs cool enough to handle.
Squeeze the roasted cloves from both bulbs into a medium bowl, add the 1 pinch of salt, and mash with a fork until they form a smooth paste.
Add the 8 ounces mascarpone (at room temperature) to the mashed garlic and stir until fully combined.
Stir in the chopped herbs — ¼ cup basil, 2 tablespoons rosemary, 2 tablespoons thyme, 2 tablespoons oregano, and 1 tablespoon parsley — until evenly distributed in the mascarpone mixture.
In a separate bowl, toss together the grated cheeses: 8 ounces provolone, 4 ounces mozzarella, and 2 ounces parmesan.
Spread the mascarpone–garlic–herb mixture evenly on the inside (one side) of each of the 8 bread slices.
Assemble 4 sandwiches: on the mascarpone-spread side of 4 slices, divide the mixed cheeses evenly among them, then top each with a second slice of bread (mascarpone side facing in).
Heat a large skillet or griddle over medium-low heat (use medium only if your pan runs cool). Place one sandwich in the dry skillet (no additional butter or oil) and cook until the bottom is golden and the cheese begins to melt, pressing gently with a spatula as it cooks, about 3–5 minutes.
Flip the sandwich and cook the second side until golden and the cheese is fully melted, another 3–5 minutes. If the bread is browning too quickly before the cheese melts, lower the heat and cover the skillet for 1–2 minutes to help the cheese melt.
Repeat steps 10–11 with the remaining sandwiches. Serve the grilled cheese sandwiches immediately.