Heat the olive oil in a large skillet over medium-high heat and add in the onions and garlic. Sauté until the garlic is fragrant, about 30 seconds.
Add the bell peppers, zucchini, salt, cumin, and black pepper. Cook until softened, about 10 minutes. Remove from heat.
In a separate skillet, melt ½ tablespoon of butter over medium heat. Place two slices of bread onto the melted butter and toast for 1-2 minutes. Repeat on the other side with another ½ tablespoon of butter.
Assemble the grilled cheese in the pan by spreading 1 tablespoon of the chimichurri sauce, and layering 1 slice of mozzarella cheese, ¾ cup fajita veggies, and an additional slice of cheese on one slice of toasted bread. Top with the other slice of toasted bread and press down with a spatula to melt the cheese and bind all the ingredients together inside the sandwich.
Flip the grilled cheese over when the mozzarella starts to melt and cook for another 2 to 4 minutes.
Repeat this process with the remaining ingredients to make all the grilled cheese sandwiches.
Slice in half and serve.
Notes
Cheese. Mozzarella has a creamy and mild flavor, but you can also use sliced Swiss, Colby jack, pepper jack, or shredded sharp cheddar.
Bread. Grilled cheeses need a thick bread with a denser crumb so it can hold up to the fillings. I like to use sourdough or rye, but you could use your favorite white bread as well.
Chimichurri. You can make a batch of my favorite chimichurri sauce or use your favorite jarred variety.