Heat butter and 1 tbsp oil in a large skillet over medium high heat. Add garlic and crushed red pepper: cook, stirring constantly until fragrant, about 1 minute. Stir in wine, salt, and lemon zest; cook, stirring occasionally, until wine is slightly reduced, about 3 minutes.
Add shrimp in a single layer to sauce in skillet; cook until shrimp are opaque and just cooked through, 1-2 minutes, flipping once halfway through cook time. Transfer shrimp mixture to a medium bowl, and tent with aluminum foil to keep warm; set aside. Wipe skillet clean.
Heat remaining 1 tbsp oil in skillet over medium. Add orzo, and cook, stirring constantly, until lightly toasted, about 1 minute. Add chicken stock and 1 cup water; bring to a simmer over high. Reduce heat to medium-low; simmer, uncovered and undisturbed until orzo is al dente and liquid is mostly absorbed, about 12 minutes. Remove from heat, and add parsley, 2 tbsp lemon juice, and 1 teaspoon tarragon. Stir orzo mixture using a fork until evenly combined
Stir remaining 2 tbsp lemon juice and remaining 2 teaspoons tarragon into reserved shrimp mixture. Spoon over orzo; cover and let stand, allowing residual heat from the orzo to warm the shrimp through, about 4-5 minutes. Uncover and garnish with additional chopped tarragon & serve