In a small pot, combine rice, 1¼ cups water (2¼ cups for 4 servings), and a pinch of salt. Bring to a boil, then cover and reduce to a low simmer. Cook until rice is tender, 15-18 minutes. Keep covered off heat until ready to serve
Cut broccoli into bite-size pieces if necessary. Trim and thinly slice scallions, separating whites from greens.
Heat a large drizzle of oil in a large pan over medium-high heat. Add broccoli; season with half the garlic powder (you’ll use the rest in the next step), a big pinch of salt, and pepper. Cook, stirring occasionally, until browned and tender, 5-7 minutes.
Turn off heat; transfer to a plate. Wipe out pan.
While broccoli cooks, rinse shrimp* under cold water, then pat dry with paper towels. Season all over with remaining garlic powder, salt, and pepper.
Heat a drizzle of oil in same pan over high heat. Add shrimp and scallion whites; cook, stirring occasionally, until shrimp are opaque and cooked through, 3-4 minutes.
Place spicy mayo in a small bowl. Add water 1 tsp at a time until mixture reaches a drizzling consistency. Season with salt and pepper.
Fluff rice with a fork; taste and season with salt and pepper.
Divide rice between shallow bowls; top with shrimp and broccoli in separate sections. Drizzle shrimp with spicy mayo; sprinkle bowls with scallion greens and sesame seeds. Serve.