Pat the shrimp dry. Moisture makes shrimp steam instead of sear. Season both sides with salt and pepper.
Heat the pan. Set a large skillet over medium-high heat. Add the olive oil and 1 tablespoon of butter.
Sear the shrimp. Arrange shrimp in a single layer and cook 1–2 minutes per side until pink and just opaque.
Remove to a plate. Don’t overcook.
Sauté the garlic. Lower heat to medium. Add remaining butter and the garlic.
Cook 30 seconds, just until fragrant.
Build the sauce. Stir in the pesto and heavy cream. Bring to a gentle simmer. The sauce should thicken slightly in 2–3 minutes.
Add Parmesan and lemon. Stir in Parmesan, lemon juice, and red pepper flakes if using.
Taste and adjust salt and pepper.
Return the shrimp. Add shrimp back to the pan. Toss to coat and warm through for about 1 minute.
Finish and serve. Top with fresh basil and extra Parmesan. Serve over your favorite low-carb base or enjoy as-is.