Pat the shrimp dry with paper towels and season lightly with 1/2 teaspoon salt and a pinch of pepper. Drying the shrimp ensures a good sear; moisture steams the shrimp and prevents browning.

Zest one lime and set zest aside. Juice both limes into a small bowl (about 3 tablespoons). Reserve. Zest delivers concentrated bright oils while the juice brings acidity and brightness to balance the cream.

Warm a large skillet over medium-high heat until hot, then add the olive oil and 1 tablespoon butter. When the butter foams and begins to brown slightly, add the seasoned shrimp in a single layer without crowding. High heat and no crowding let the shrimp develop a golden sear (Maillard reaction) in 1–1.5 minutes per side.

Sear shrimp 1–1½ minutes on the first side, then flip and cook another 30–45 seconds until just opaque and curled. Remove shrimp to a plate — they will finish cooking briefly in the sauce. Avoid overcooking; shrimp become rubbery if cooked too long.

Lower heat to medium. Add the remaining 1 tablespoon butter to the same skillet. Add the minced shallot and cook 1–2 minutes until softened and translucent. Shallot sweats and sweetens at medium heat, building a savory base for the sauce.

Add the minced garlic, smoked paprika and red pepper flakes; cook 20–30 seconds until fragrant. Toasting the spices briefly in the fat blooms their oils and deepens flavor — be careful not to burn the garlic.

Pour in the heavy cream and stir, scraping any browned bits from the pan. Bring to a gentle simmer (not a rolling boil). The cream will pick up the fond and thicken as it reduces; simmering concentrates flavor while keeping the texture silky.

Simmer the cream sauce 3–4 minutes until it thickens slightly. Stir in the lime juice (start with 2 tablespoons; taste and add more for brightness if you like), smoked paprika, remaining 1/2 teaspoon salt and 1/4 teaspoon pepper. Acid from the lime brightens the richness — add gradually so the sauce doesn’t split.

Return shrimp and any accumulated juices to the pan and gently warm through 1–2 minutes, spooning the sauce over the shrimp. Finish with the lime zest and taste to adjust salt, pepper and extra lime if desired. Warming here melds flavors without overcooking the shrimp.

Remove from heat and, if desired, swirl in a 1 teaspoon knob of cold butter for gloss and mouthfeel. Sprinkle with chopped parsley or cilantro and serve immediately. The final butter enriches and smooths the sauce while the herb adds freshness and color.

Serving suggestion: Serve over steamed rice, creamy polenta, buttered pasta, or with crusty bread to soak up the sauce. The recipe as written serves 4 as a main with a starch or 6 as an appetizer.