Adjust rack to top position and preheat oven to 425 degrees. Wash and dry all produce. Trim, peel, and halve cucumber lengthwise; thinly slice crosswise into half-moons. In a small bowl, combine cucumber, vinegar, ½ tsp sugar (1 tsp for 4 servings), and a pinch of salt. Set aside. Trim and thinly slice scallions, separating whites from greens. Quarter lemon.

In a second small bowl, combine mayonnaise, jam, sriracha, half the garlic powder, 1 tsp water (2 tsp for 4 servings), and a pinch of salt. Melt 1 TBSP butter in a small pot over medium-high heat. Add scallion whites; cook, stirring, until softened, 1 minute. Add rice, ¾ cup water (1½ cups for 4), and a pinch of salt. Bring to a boil; cover and reduce to a low simmer. Cook until rice is tender, 15-18 minutes. Keep covered off heat until ready to serve.

While rice cooks, cut broccoli florets into 1-inch pieces, if necessary. Toss on a baking sheet with a drizzle of oil, half the sesame seeds (save the rest for serving), salt, and pepper. Roast on top rack until golden brown and crispy, 15-20 minutes. Remove from oven and toss with a squeeze of lemon juice and half the scallion greens.

Meanwhile, rinse shrimp under cold water; pat very dry with paper towels. Season with salt. In a large bowl, combine tempura mix, remaining garlic powder, salt (we used ½ tsp kosher salt; 1 tsp for 4 servings), and ⅓ cup cold water (⅔ cup for 4). (TIP: If needed, add more water 1 TBSP at a time until it reaches a pancake-batter-like consistency.) Stir shrimp into batter until fully coated. Heat a ¼-inch layer of oil in a large, heavy-bottomed pan over medium-high heat.

Once oil is hot enough that a drop of batter sizzles when added to the pan, working in batches, add coated shrimp in a single layer. Cook until golden brown and cooked through, 2-3 minutes on the first side and 1-2 minutes on the second side. Using a slotted spoon, transfer to a paper-towel-lined plate. Immediately season with salt and pepper.

Fluff rice with a fork; stir in 1 TBSP butter and season with salt and pepper. Divide between bowls. Top with shrimp and quick pickles (draining first). Drizzle shrimp with sauce; top with remaining scallion greens and sesame seeds, plus a pinch of chili flakes. Serve with broccoli and remaining lemon wedges on the side.