Rinse the jasmine rice under cold water until the water runs clear, then cook it according to package directions and set it aside.
Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the minced garlic and sliced chili and stir for 30 seconds until fragrant.
Add the shrimp to the pan and cook for 2 minutes, stirring often, until they begin to turn pink.
Toss in the broccoli florets and stir-fry for 3 to 4 minutes until the broccoli is bright green and just tender.
Pour in the fish sauce and soy sauce, then stir everything together for another minute so the shrimp finish cooking and the sauce coats the ingredients.
Remove the pan from the heat and fold in the Thai basil leaves until they wilt slightly.
Divide the cooked jasmine rice among four plates or bowls and top each with the shrimp stir-fry.