In a large bowl, combine shrimp, 2 tablespoons oil, and paprika. Cover and refrigerate for 30 minutes.
Meanwhile, make the stir fry sauce. In a small bowl, whisk the sugar, red wine vinegar, orange juice, chicken broth, ketchup, soy sauce, and sweet chili sauce. Set aside.
Heat 1 tablespoon oil in a large cast iron skillet over high heat until just smoking. Add the shrimp in batches to not overcrowd the pan and cook without stirring, until the bottom of the shrimp are browned at the edges, about 2 minutes. Turn the shrimp over, add the garlic, and cook just until opaque and nearly cooked through, about 30 seconds; transfer to a plate.
In the same pan used to cook the shrimp, heat remaining 2 tablespoons of oil. Add broccoli, peppers, and carrots; cook 2-3 minutes until veggies start to soften. Add the sauce and bring to a boil. Make the cornstarch slurry, by whisking the cornstarch and water until smooth. Pour the slurry in the pan, as well as the snow peas, and reduce the heat to a simmer until sauce has thickened, 1-2 minutes.
Garnish with green onions and sesame seeds. Serve over noodles or white rice. Enjoy!