Preheat the oven (or toaster oven) to 400 degrees. Line a baking sheet with foil.
Lightly rub olive oil on the surface of each poblano chile. Place them on the baking sheet and bake for 15-20 minutes until the outer skin blackens and blisters throughout. You may need to rotate them half way through to roast them evenly.
Remove them from the oven and place them in a bowl. Cover with a kitchen towel and set aside to cool completely.
Once cooled, rub off or peel and discard the outer blackened skin under running water (don't worry about needing to get all of it), carefully tearing the poblano peppers open and pulling out the seed pods and stems inside. Rinse all the seeds away.
Finely dice the roasted peppers and set aside.
To Prep the Squash Blossoms:
Discard the stems and stamen from each squash blossom. Quickly rinse off the squash blossoms and roughly chop them up.
To Prepare the Quesadillas:
In a non-stick pan, heat 1/2 tbsp of oil on medium heat.
Add the minced garlic and fry until fragrant (~30 seconds), mixing frequently.
Add the sliced onions and saute until they start to turn translucent.
Add the chopped squash blossoms, chopped roasted poblano peppers, and halved sweet cherry tomatoes.
Season with salt to taste.
Cook for an additional few minutes until the squash blossoms just start to wilt and tomatoes start to cook in.
Mix in the chopped cilantro, turn off the heat, and set the mixture aside.
In another non-stick pan on low-medium heat, grill two corn tortillas on both sides using a little olive oil or vegan earth balance butter. Remove one corn tortilla and set aside. Top the other corn tortilla in the pan with a layer of the prepared squash blossom mixture and some vegan pepper jack shreds.
Place the other grilled corn tortilla, which was set aside, on top and grill once more on the heated pan on both sides in order to allow the vegan pepper jack cheese shreds to melt.
Remove from heat, cut into 4 pieces using a pizza cutter, and enjoy with your favorite hot sauce (such as Cholula).
Notes
Vegan Pepper Jack Cheese - I recommend using Follow Your Heart pepper jack slices for these quesadillas. You can also use Diaya brand pepper jack shreds.