Preheat your oven to 375°F and line a baking sheet with foil or parchment paper. Toss the small red potatoes with 3 tablespoons of olive oil and 1½ teaspoons of kosher salt, ensuring they're evenly coated. Spread them in a single layer on the prepared baking sheet and roast for 40-50 minutes until they're tender when pierced with a fork. Once roasted, remove from the oven and let them cool completely—this makes them easier to handle when flattening. I like to chill them for at least 30 minutes before grilling, as cold potatoes hold their shape better when pressed.

While the potatoes are roasting, prepare your flavor base by whisking together 4 tablespoons of olive oil with the minced fresh rosemary, minced garlic cloves, ½ teaspoon of garlic salt, ½ teaspoon of freshly cracked black pepper, and ½ teaspoon of smoked paprika. Let this mixture sit for a few minutes so the flavors can meld and infuse the oil. This aromatic oil is what gives the grilled potatoes their signature flavor, so don't skip this step.

Once the roasted potatoes from Step 1 are cooled and chilled, carefully flatten each one to about ¾ inch thickness using the bottom of a measuring cup or a potato masher. Work gently to avoid breaking them apart. Arrange the flattened potatoes on a clean surface or plate, then generously brush both sides with the garlic rosemary oil mixture from Step 2, making sure each potato gets an even coating of the aromatic oil and seasonings.

Heat your grill to medium-high heat. Once hot, carefully place the oiled and flattened potatoes directly on the grill grates. Grill for 3-4 minutes on the first side until you get nice golden grill marks, then flip carefully and grill the other side for another 3-4 minutes. The potatoes should develop a crispy, charred exterior while staying creamy inside. Transfer the grilled potatoes to a serving plate, immediately sprinkle with the grated Parmesan cheese while they're still hot so it melts slightly, and finish with a garnish of fresh chopped parsley.