Heat half of a gas grill for direct, medium-high heat (about 400ºF), or heat a charcoal grill for two-zone cooking. Place a small cast iron skillet, oven-safe frying pan, or grill-safe baking dish that's about the same size as 1 (8-ounce) piece sharp provolone cheese on the grates of the unlit side of the grill while it is heating. Meanwhile, make the chimichurri.

Prepare the following, adding each to a mini or regular food processor fitted with the blade attachment as you complete it: Smash and peel 1 garlic clove. Pick the leaves from 1 small bunch fresh parsley until you have 1 packed cup. Pick the leaves from 3 fresh oregano sprigs until you have ¼ packed cup.

Add ¼ cup olive oil, 1 tablespoon red wine vinegar, ¼ teaspoon kosher salt, and ¼ teaspoon red pepper flakes to the food processor. Pulse, scraping down the sides of the bowl occasionally, until blended but still a little chunky, 25 to 30 pulses.

Lightly brush one side of the cheese with olive oil. Place, oil-side down, on the direct-heat side of the grill. Grill uncovered until the edges start to melt and soften, 30 seconds to 1 minute. Use a thin metal spatula to lift and flip the provolone over into the skillet, oil-side up.

Cover and grill, until the cheese is very soft and melty, 6 to 8 minutes more. Carefully transfer the skillet to a heat-proof plate or surface. Spoon some of the chimichurri over the provoleta and serve immediately with crusty bread and the remaining chimichurri.