Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Cut the chicken breast, zucchini, and red bell pepper into uniform 1-inch bite-sized pieces.
Place the chicken and chopped vegetables on the prepared baking sheet and toss with 0.5 tbsp of the olive oil, dried oregano, sea salt, and black pepper.
Roast in the oven for 20-22 minutes until the chicken is fully cooked and the vegetables are tender with lightly browned edges.
While the chicken and vegetables roast, whisk together the remaining 0.5 tbsp of olive oil, balsamic vinegar, and Dijon mustard in a small bowl to create the vinaigrette.
Remove the baking sheet from the oven and allow the chicken and vegetables to cool completely in the refrigerator for at least 30 minutes.
In a large bowl or meal prep container, layer the mixed greens, top with the chilled roasted chicken and vegetable mixture, and drizzle with the balsamic vinaigrette just before eating.