Heat butter and 1 tablespoon oil in a large skillet over medium-high. 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 to 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 the remaining one tablespoon of oil in the skillet over medium heat.
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 tablespoons lemon juice, and 1 teaspoon tarragon.
Stir orzo mixture using a fork until evenly combined.
Stir the remaining two tablespoons of lemon juice and the remaining two teaspoons of tarragon into the reserved shrimp mixture.
Spoon shrimp mixture over orzo; cover and let stand, allowing residual heat from the orzo to warm the shrimp through, 4 to 5 minutes.
Uncover and garnish with additional chopped tarragon; serve immediately.