Prepare the Shrimp. Start by patting the shrimp dry with paper towels. Dry shrimp will result in a better sear and crispier texture. In a bowl, toss the shrimp with a pinch of salt and set aside.
Stir-Fry to Perfection. Heat vegetable oil in a large skillet or wok over medium-high heat. Add the minced garlic and ginger, stirring frequently until fragrant, about 1 minute. Add the chili paste and stir to combine. Add the shrimp to the skillet in a single layer. Cook for 2-3 minutes on each side until the shrimp is pink and opaque. Remove the shrimp from the skillet and set aside.
Create the Sauce. In the same skillet, add soy sauce, rice vinegar, and brown sugar. Stir until the sugar dissolves and the sauce begins to thicken. Return the shrimp to the skillet and toss to coat in the sauce.
Garnish and Serve. Transfer the coated shrimp to a serving platter. Drizzle with sesame oil and garnish with chopped green onions for a burst of color and added freshness.