In a shallow dish, add the Armagnac to the shrimp; marinate for 15 minutes.
Remove the shrimp from the marinade and drain lightly on paper towels. Season with salt and pepper.
In a large skillet, heat 2 tablespoons of the oil until shimmering. Add half of the shrimp and stir-fry over high heat until browned on both sides and cooked through, about 1 minute total. Transfer to a platter and repeat with the remaining oil and shrimp. Serve immediately.