Preheat oven to 350 degrees F.
On a baking sheet, lay out okra in a single layer; drizzle with 2 tablespoons of oil and season with kosher salt and pepper, toss to coat.
Place okra on the top rack of the oven and roast for 25 to 30 minutes, turning on occasion.
Bring 3 ½ cups of water to a boil in a small pot. Slowly add grits, butter, and ½ tablespoon of salt to the water. Stir until the mixture returns to a boil, ensuring an even consistency. Reduce heat to medium-low, cover, and cook for 5-7 minutes, stirring on occasion until mixture is thick.
Add Parmigiano-Reggiano cheese and heavy cream to grits and stir until well combined.
Meanwhile, preheat a cast iron skillet over medium heat and season salmon filets with kosher salt and pepper. Add 2 tablespoons of olive oil to the skillet followed by the salmon filets; cook, undisturbed, for 3 to 4 minutes. Squeeze the juice of ½ lemon over the top the filets; flip.
Cook filets for 2 to 3 more minutes, or until internal temperature reaches 135 degrees F; remove from heat.
Plate a generous portion of grits in the center of the plate, followed by the salmon and okra at either side. Sprinkle with diced red pepper for garnish.