In a small bowl, combine the Greek yogurt with half of the fresh mint, half of the minced garlic, 1/4 teaspoon salt, and black pepper to taste. Stir to combine. Transfer this mixture to a small serving bowl. Swirl in 1 teaspoon of olive oil on top and garnish with the remaining fresh mint.
Preheat your grill or grill pan to medium-high heat. Once hot, lightly oil the grates to prevent sticking.
In a large bowl, toss the prepared vegetables (bell peppers, red onion, asparagus, yellow squash, and zucchini) with 2 tablespoons of olive oil, lemon juice, the remaining minced garlic, Za'atar seasoning, 1/2 teaspoon kosher salt, and 1/4 teaspoon black pepper. Toss until all vegetables are evenly coated.
Grill the seasoned vegetables, turning occasionally, until they are tender and lightly charred. This should take approximately 6 to 10 minutes, depending on your grill and the thickness of the vegetables. Arrange the grilled vegetables on a platter and serve immediately with the yogurt mint sauce.
Notes
This recipe is easily adaptable to different vegetables. Feel free to use other seasonal vegetables like broccoli, cauliflower, or cherry tomatoes. Ensure vegetables are cut into similar sizes for even grilling.