Preheat the Pan: Position an oven rack in the center and preheat to 425°F (220°C). Place a large, rimmed baking sheet in the oven to get hot.
Make the Yogurt Drizzle: In a small bowl, whisk together ½ cup of the non-fat Greek yogurt, the juice from half of the lemon (about 1 ½ tbsp), and the agave nectar. Season with a pinch of black pepper and set aside in the refrigerator.
Season the Vegetables: In a large bowl, combine the asparagus, mushrooms, and cherry tomatoes. Drizzle with 2 tablespoons of olive oil and add the minced garlic, dried oregano, ½ teaspoon of the salt-free seasoning, and ¼ teaspoon of black pepper. Toss well to coat.
Prepare the Chicken: Place the chicken cutlets between two sheets of parchment paper and gently pound them to a uniform ½-inch thickness. This ensures they cook quickly and evenly.
Mix the Coating: In a shallow dish, combine the crushed no-salt-added crackers, nutritional yeast, garlic powder, the remaining ½ teaspoon of salt-free seasoning, and the remaining ¼ teaspoon of black pepper.
Coat the Chicken: Place the remaining ⅓ cup of non-fat Greek yogurt in a separate bowl. Pat the chicken cutlets dry, dip each one into the yogurt to coat all sides, then press it firmly into the cracker mixture to create a thick, even crust.
Roast Everything: Carefully remove the hot baking sheet from the oven. Arrange the coated chicken on one half and spread the seasoned vegetables on the other. Drizzle the last tablespoon of olive oil over the chicken. Roast for 22 to 26 minutes, until the vegetables are tender and the chicken is golden, crispy, and cooked through (165°F / 74°C).
Garnish and Serve: Remove the pan from the oven. Zest the remaining lemon half over the chicken and vegetables. Serve immediately, drizzling each portion with the chilled yogurt sauce and a generous sprinkle of fresh parsley.