Preheat the oven to 425 degrees.
Place the zucchini, squash, bell peppers, mushrooms, onion, eggplant and poblanos in a large bowl. Drizzle the oil over the vegetables. Add a few pinches of salt and freshly ground black pepper. Toss the vegetables to coat evenly.
Wrapping foil around your cookie sheet helps with easy clean up. Lightly spray the pan with a nonstick spray such as Pam. Pour the vegetables onto the pan and spread them even. Use 2 pans if necessary, so that your veggies are mostly in one layer.
Bake the vegetables in the preheated oven for 20 to 25 minutes, or until softened. If you’d like some caramelization on your veggies, allow to bake a little longer, checking every few minutes to not burn them.
Preheat your panini press, or you can heat a shallow skillet over medium to medium-high heat. (If you use a pan instead of a Panini, you’ll have to carefully flip the sandwich in order to toast the other side.)
Place 2 slices of bread on a plate or cutting board. On one side of a piece of bread spread 2 tablespoons of the pesto.
(You should have enough veggies to make 4 sandwiches.) Place a quarter of the roasted vegetables on top of the pesto, top with 2 slices of cheese, then place with another piece of bread.
Place the sandwich on the preheated panini press and close the lid. (You can continue to hold down the lid with some gentle pressure, or allow the machine to work on its own. It might brown quicker and get those nice lines we all like if you do hold it down for a couple of minutes. Either way is fine.)
Allow the panini press to brown the bread, approximately 2-5 minutes, depending on your appliance.
Once browned, remove the sandwich and cut it in half using a serrate knife. Continue to make the remaining sandwiches.
Serve while still very warm.