Begin by combining the marinade mix with beer. Reserve 2 Tbsp. of the marinade. Chop or slice veggies and place all but the tomatoes in a large mixing bowl. Pour marinade mix (except for reserved) over veggies. Stir and place in refrigerator for about 30 minutes.
Combine Greek yogurt and mayonnaise with the reserved 2 Tbsp. marinade mix. Refrigerate for about 45 minutes.
Remove veggies from fridge. Heat 1 Tbsp. olive oil in a frying pan; add veggies and cook about 5-8 minutes or until zucchini softens. Remove from heat.
Prepare tortillas. Spread about 2 Tbsp. yogurt mixture on tortillas. Top half of tortilla with about ½ cup of the veggie mixture (use a slotted spoon for scooping to drain the mixture). Top with tomatoes and feta cheese, if desired. Fold tortillas in half and place on grill.
Grill for 15-25 minutes, carefully turning them periodically. Be sure to keep your heat low to medium to avoid burning the quesadillas.
To serve, place quesadillas on a cutting board. Using a pizza cutter, cut into triangles and serve! Use extra yogurt mixture as a dipping sauce.