Wash and dry all produce. Preheat oven to 450 degrees (if you'd like to grill the burgers and buns, heat the grill to high, too). Mince or grate garlic until you have 1/2 tsp (you’ll have a clove left over). Halve, peel, and thinly slice onion. Cut zucchini into 3-inch-long sections, then halve each piece lengthwise. Cut halves into thin wedges.

In a small bowl, mix together 3 TBSP mayonnaise (we sent more) and as much of the garlic as you like (start with a pinch and go up from there). Season with salt and pepper.

Heat a large drizzle of oil in a large pan over medium heat. Add onion and cook until nicely browned, 8-10 minutes, tossing occasionally. Stir in balsamic vinegar and 2 tsp sugar. Continue cooking until syrupy, 1-2 minutes more. Season with salt and pepper. Remove from pan and set aside in another small bowl. Wash out pan.

While onion is cooking, toss together zucchini and 1 TBSP aioli in a medium bowl until wedges are evenly coated. Add panko, oregano, and a large pinch of salt and pepper and toss so that crumbs stick to zucchini. Spread on a lightly oiled baking sheet. Bake in oven until panko is golden-brown, about 15 minutes, tossing halfway through. TIP: It’s OK if not all the breadcrumbs stick.

Heat a large drizzle of oil in pan you cooked onion in over medium-high heat (skip this if grilling). Shape beef into four patties (make them slightly wider than the buns). Season with salt and pepper. Add to pan or grill and cook until burgers almost reach desired doneness, 3-5 minutes per side. Top with cheese. Cover pan or grill and continue cooking until cheese melts, about 1 minute.

While burgers cook, split buns in half and place on another baking sheet (skip the sheet if grilling). Toast in oven or on grill until golden, about 3 minutes. Spread ketchup and remaining aioli onto buns. Fill each with a burger and as much onion jam as you like. Serve with zucchini fries on the side.