Step 1

Heat broiler. Combine shallot, vinegar, sugar, and a pinch of salt and pepper in a small bowl. Stir to combine; set aside.

Step 2

Trim and peel broccoli stem. Remove stem from crown and finely chop. Cut crown into florets, then coarsely chop into bite-size pieces.

Step 3

Heat oil in a large ovenproof skillet over medium-high. Add broccoli; season with salt. Cook, stirring occasionally, until browned in spots, about 3 minutes. Reduce heat to medium, add ¼ cup water, and cover. Cook until tender, about 2 minutes. Reduce heat to low and uncover. Grate in garlic; add reserved shallot mixture. Cook, stirring, until vinegar is mostly evaporated, about 15 seconds. Transfer to a bowl. Reserve skillet.

Step 4

Mix mayonnaise and chili sauce in a small bowl. Taste and add more chili sauce if desired.

Step 5

Broil bread, cut side up, in reserved skillet until lightly toasted, about 1 minute (watch carefully!). Remove from oven and spread mayo mixture over. Spoon broccoli mixture on top, going all the way to the edges (don’t be afraid to pile it on). Drape a slice of cheese over (tear in half if needed).

Step 6

Broil, watching carefully, until cheese is bubbling and browned, about 3 minutes. Season with pepper.