Wash and dry all produce. If grilling, heat a grill for direct heat. Zest 1 tsp zest from lemon, then cut in half. Squeeze 2 tsp juice into a small bowl. Strip and finely chop enough rosemary leaves from stems to give you 1 TBSP. Mince or grate garlic.

Place 2 TBSP butter in another small, microwave-safe bowl. Microwave on high until just soft, about 10 seconds. (TIP: Make sure not to melt butter.) Stir in lemon zest, 1/4 tsp sugar, and a pinch of salt. Set aside. To bowl with reserved lemon juice, add mayonnaise, a pinch of garlic, 1 tsp rosemary, and a pinch of pepper. Stir to combine.

Slice tomato into 1/3- to 1/2-inch-thick rounds. Peel onion, then slice into 1/2-inch-thick rounds. Carefully cut or break corn ears in half. Place beef, Parmesan, remaining garlic and rosemary, a pinch of pepper, and a few large pinches of salt in a large bowl. Mix until just combined, then shape into four 4-inch-wide patties.

Brush grill grates with olive oil. (TIP: If cooking indoors, heat a drizzle of olive oil in two grill pans or large pans over medium-high heat; use one for the veggies in this step and use the other for the patties.) Add corn and cook, turning occasionally, until charred all over, about 10 minutes. Add onion rounds and cook until charred, about 3 minutes per side. Add tomato and cook until charred, about 2 minutes per side.

Add patties to grill or other pan and cook to desired doneness, 3-5 minutes per side. If you’d like toasted buns, split buns in half and grill cut-side down until light golden, 1-2 minutes.

Spread buns with mayonnaise mixture and fill with patties, tomato, and onion. Dollop corn with butter mixture and serve on the side.