In a medium bowl, toss together chopped shrimp, 1 tablespoon soy sauce, and brown sugar. Set aside.
Melt 1 tablespoon butter in a large skillet over medium-high heat. Add the shrimp and cook, stirring frequently, until just cooked through, about 1 minute. Transfer to a bowl.
Add an additional 1 tablespoon butter to the empty skillet. Melt the butter over medium-high heat. Add eggs and stir with a rubber spatula until set but still wet, about 15 seconds. Push the eggs to one side of the skillet. Add remaining 2 tablespoons butter, the white parts of the green onions, and the garlic to the skillet; cook until fragrant (about 15 seconds).
Add rice and stir to break up any clumps or large pieces of egg. Cook until the rice begins to sizzle loudly, about 3 minutes.
Stir in remaining 3 tablespoons soy sauce, hoisin sauce and sesame oil; stir constantly for 2 minutes.
Stir in peas, shrimp and any accumulated juices in the bowl, and green parts of the green onions. Cook just until heated through, about 1 minute. Taste and season with salt and pepper or additional soy sauce, if desired.