Nutty brown butter is a natural pairing with grits, and grits are a natural pairing with shrimp. The whole is even greater than the sum of its parts when this hearty dish comes together. You'll love the way smoked Gouda infuses the rich, creamy grits topped by savory brown butter sauce. Naturally.
Trim and slice whites of green onions into ½" pieces. Thinly slice remaining green onions on an angle. Halve grape tomatoes. Zest lemon, halve, and juice. Rinse shrimp, pat dry, and season with a pinch of salt and pepper.
Cook the Grits
When water is boiling, whisk in grits in a steady stream to avoid clumping. Stir until consistency is slightly thicker than pancake batter. Reduce heat to medium-low and cook 2 minutes. Stir in 1 Tbsp. butter and smoked Gouda. Season to taste with salt and pepper. Remove from heat and keep warm.
Sear the Shrimp
Place a large pan over medium-high heat and add 1 tsp. olive oil. Add shrimp and sear on one side until browned, about 2 minutes, then remove to a plate (shrimp will finish cooking later). Reserve pan for next step (no need to wipe clean).
Begin the Brown Butter Sauce
Return pan to medium heat and add remaining butter. Allow butter to melt, then continue cooking until it begins to smell nutty and turn golden, about 3 minutes. Butter browns shortly after it stops sizzling, so listen closely for when it's ready. Stir in white parts of green onions, mustard, lemon zest, 1 Tbsp. lemon juice, red pepper flakes (start with a ¼ tsp., taste, and add more, if desired), and a pinch of salt and pepper. Return shrimp to pan and cook 2 minutes or until shrimp is opaque and reaches a minimum internal temperature of 145 degrees.
Make the Salad
In a medium mixing bowl, combine 2 tsp. lemon juice, 1 Tbsp. olive oil, and salt and pepper (to taste). Stir, add arugula and tomatoes, and toss together.
Plate the Dish
Divide grits between two shallow bowls and sprinkle with smoked paprika (to taste). Add shrimp, spoon butter sauce over grits, and garnish with remaining green onions. Serve arugula and tomato salad on side.