Wash and dry all produce. Preheat broiler to high or oven to 500 degrees, adjusting racks so that one is positioned directly beneath flame and other is in position furthest away. Slice eggplant into 1/2-inch-thick rounds. Halve, peel, and finely dice onion. Mince garlic. Cut baby broccoli lengthwise into thin sticks. Thinly slice mozzarella.

Brush eggplant all over with a large drizzle of olive oil. Season with salt and pepper. Place on a baking sheet in a single layer. Broil (or bake) on rack closest to flame until browned and tender, 15-20 minutes, flipping halfway through.

Meanwhile, heat a drizzle of olive oil in a large pan over medium heat. Add onion and 1 tsp Italian seasoning (we sent more). Cook, tossing, until translucent, 3-4 minutes. Toss in garlic and cook until fragrant, 2 minutes. Stir in tomatoes, 1/2 tsp sugar, and 1/4 cup water. Let simmer until eggplant is ready. Season with salt and pepper.

Toss baby broccoli on another baking sheet with a drizzle of olive oil and a pinch of salt and pepper. Roast in oven on rack furthest away from flame until tender and crisped at edges, 10-12 minutes.

Remove eggplant from oven once done. Spread a little bit of sauce on top of each slice, then top with mozzarella. Return to broiler (or oven) and continue broiling until mozzarella is browned in spots and melted, about 5 minutes.

Split buns in half. Toast in oven until lightly toasted, about 2 minutes (you can add the buns to the same sheet as the baby broccoli). Fill buns with eggplant slices. Serve with baby broccoli to the side.