ROAST THE VEGETABLES: Preheat the oven to 400F. Prepare 2 quarter sheet pans (or put the carrots on one side and the potatoes on the other of a half sheet pan) by spraying with cooking spray or lining with foil. Potatoes: In a medium bowl, toss the potatoes with a drizzle of olive oil and a ¼ teaspoon each kosher salt, fresh ground pepper, and dried thyme. Turn the potatoes out onto the prepared pan and flip them cut side down. Carrots: In a medium bowl, toss the carrots with the melted butter and sprinkle generously with kosher salt. Turn the carrots out onto the prepared pan. Roast for 30 minutes or until tender, turning once midway through roasting. The carrots may take a few minutes extra, depending on how thickly you sliced them. If veggies are done before fish, cover lightly and set aside until serving. (I like these vegetables roasted differently and separately because I like buttered carrots. If you’d rather, you can season them the same, mix them all together with olive oil, and cook them together.)
COOK THE ROCKFISH: 10 minutes before the vegetables are done, heat a large, nonstick skillet over medium heat and add the slivers of lemon. Cook two minutes. Meanwhile, pat dry the fish fillets. Season one side with salt and paprika and the other with garlic salt and black pepper, patting the spices into the fish. Add the seasoned fillets to the pan and cook undisturbed for about 3 minutes or until golden brown. Turn and cook the other side until it’s firm and opaque—another 2 or 3 minutes. FDA indicates cooking fish to 145F on an instant read thermometer. I take it off at 135F or 140F and let it rest briefly to insure a moist fillet.
MAKE THE CAPRESE: While the fish cooks, stir together the tomato, basil, and mozzarella in a small bowl; add a pinch of crushed red pepper. Set aside until the fish is cooked, if necessary.
PLATE THE MEAL: Place a cooked fish fillet and a lemon sliver or two (cooked lemon rind is edible) at the center of a dinner plate or shallow bowl. Add roasted potatoes and carrots. Top the fish with a generous spoonful of caprese and snuggle up a fresh lemon wedge to the side. Repeat. Serve hot or warm.