Preheat a grill or grill pan over medium-high heat.
In a large bowl, toss the zucchini, yellow squash, red bell pepper, and red onion with olive oil, salt, and pepper.
Grill the vegetables for about 4-5 minutes on each side, or until they are tender and have nice grill marks. Remove from the grill and set aside.
While the vegetables are grilling, toast the slices of bread on the grill until golden brown, about 2-3 minutes per side.
To assemble the sandwich, place a generous amount of grilled vegetables on one slice of toasted bread. Tear the burrata cheese into pieces and place it on top of the vegetables.
Add a handful of arugula on top of the burrata, and drizzle with balsamic glaze if desired.
Top with another slice of toasted bread, press down gently, and slice in half to serve.