Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper.
Toss the jalapenos with 1 tablespoon olive oil and some salt and pepper and lay skin-side up on the prepared baking sheet. Bake until the skins are blistered, 10 to 15 minutes. Put the jalapenos in a plastic baggie to let the skins loosen. Pull off the skins and remove a majority of the seeds and ribs. Set aside.
Mix the Cheddar and mascarpone in a bowl and spread the mixture on one side of each slice of bread. Place the jalapenos on half of the slices, then top with the remaining slices, cheese-sides in.
Heat 1/2 tablespoon olive oil and 1 tablespoon butter on a flat griddle over medium heat. Grill one side of the sandwiches until golden, about 5 minutes. Flip the sandwiches and add the remaining 1/2 tablespoon oil and 1 tablespoon butter to the griddle. Cook on the second side until the outsides are golden and the insides are all melty and gooey, another 5 minutes.