Heat the olive oil and 1 tablespoon of the butter in a large deep skillet over medium-high heat until the butter foams. Season the shrimp with 1/2 teaspoon of the salt and 1/4 teaspoon of the pepper. Sear 1–2 minutes per side, just until pink and opaque. Remove to a plate — they finish cooking later, so pull them early.

Reduce the heat to medium. Add the remaining 2 tablespoons of butter, the garlic, and the red pepper flakes; cook 30 seconds until fragrant. Stir in the dry orzo and toast 1–2 minutes, stirring, until lightly golden at the edges. This quick toast is what gives the orzo its nutty flavor and helps it stay creamy instead of mushy.

Pour in the white wine (or broth), scraping up any browned bits from the shrimp. Let it bubble for about a minute.

Stir in the chicken broth, Italian seasoning, and the remaining 1/4 teaspoon salt and 1/4 teaspoon pepper. Bring to a lively simmer, then reduce to a steady bubble and cook uncovered, stirring often, until the orzo is al dente and most of the liquid is absorbed, about 8 minutes. Orzo cooks in roughly 8 minutes — that speed is what keeps this dinner at 20 minutes.

Reduce the heat to low. Stir in the lemon zest and juice, the Parmesan, and the remaining 1 tablespoon of butter until the butter melts into a glossy sauce. Return the shrimp (plus any juices on the plate) to the skillet and toss to warm through, 1–2 minutes.

Off the heat, shower with parsley and extra Parmesan. Serve straight from the skillet with lemon wedges.