Preheat your oven to 400°F and lightly coat a large sheet pan (approximately 18x13 inches) with cooking spray. While the oven heats, cut the broccoli into 1-inch florets and chop the carrots into bite-sized pieces. In a small bowl, whisk together the balsamic vinegar and Italian dressing to create your sauce base—set aside 1/3 cup for marinating the chicken and reserve the remaining sauce for serving. In another small bowl, combine the Italian seasoning, garlic powder, smoked paprika, and a pinch of salt and pepper to create your spice blend.
Pat the chicken tenderloins dry with paper towels, then cut them into small strips (about 2-3 inches long). Place the chicken strips in a resealable bag or shallow dish and pour the reserved 1/3 cup balsamic-dressing sauce over them. Toss gently to coat evenly, then refrigerate for 30 minutes. This marinating time allows the flavors to penetrate the chicken while you prepare and roast the vegetables.
Spread the chopped broccoli and carrots on your prepared sheet pan in a single layer. Drizzle with olive oil and sprinkle the spice blend from Step 1 evenly over the vegetables, then toss to coat thoroughly. Roast in the preheated 400°F oven for 10-15 minutes, stirring halfway through, until the vegetables begin to soften and show light browning on the edges. I like to give them a good toss at the halfway point to ensure even cooking and better caramelization.
Remove the sheet pan from the oven and carefully push the roasted vegetables to the sides of the pan, creating a clear center space. Arrange the marinated chicken strips in a single layer in the center of the pan, then scatter the cherry tomatoes around and over everything. Drizzle the remaining 1/3 cup balsamic sauce over the chicken (reserve any extra for serving), making sure each piece gets some of the glaze.
Return the pan to the 400°F oven and bake for 7-15 minutes, depending on the thickness of your chicken strips, until the chicken is cooked through and no longer pink in the center (internal temperature should reach 165°F). The exact time depends on how thin you cut your chicken—thinner strips will finish faster. Remove from the oven and let cool for 2-3 minutes, then garnish generously with fresh parsley and serve directly from the pan with any reserved sauce on the side for drizzling.