Preheat the oven to 425°F (220°C). Line a baking sheet with parchment paper and set aside.

In a bowl, toss the halved jalapeños with 1 tablespoon of olive oil, salt, and black pepper. Arrange the jalapeños skin-side up on the prepared baking sheet. Roast for 10 to 15 minutes, or until the skins are blistered. Transfer the jalapeños to a plastic bag and allow them to steam for approximately 5 minutes. Remove and discard the skins, then remove most of the seeds and ribs. Slice the jalapeños and set aside.

Spread the mascarpone cheese evenly over four slices of bread. Sprinkle the shredded cheddar evenly over the remaining four slices. Divide the sliced jalapeños evenly among the sandwiches. Close the sandwiches and spread the softened butter evenly over both sides of each sandwich.

Heat the remaining olive oil on a flat griddle or large skillet over medium heat. Place the sandwiches onto the hot surface and cook until the first side is golden brown. Turn the sandwiches over and continue cooking until the second side is golden and the cheese is fully melted. Remove from heat and serve immediately.