Preheat oven to 425°F (220°C). Line a large rimmed sheet pan with parchment paper or foil. For extra-crispy potatoes, place the pan in the oven to preheat as well.
In a small bowl, combine smoked paprika, garlic powder, Italian seasoning, onion powder, dried oregano, ½ teaspoon salt, and ¼ teaspoon black pepper. Stir until evenly blended.
Halve baby potatoes (quarter large ones). In a large bowl, toss with 1½ tablespoons olive oil, half the seasoning blend, minced garlic, and ¼ teaspoon salt. Spread cut-side down on the hot pan and roast alone for 10-15 minutes.
Pat chicken breasts completely dry with paper towels. If thicker than 1 inch, pound to even thickness. Place in the large bowl with 1½ tablespoons olive oil, remaining seasoning blend, and lemon juice. Toss to coat thoroughly.
In the same bowl, toss broccoli, bell pepper, and onion with remaining 1 tablespoon olive oil, ¼ teaspoon salt, and ¼ teaspoon pepper until evenly coated.
Remove pan from oven. Place seasoned chicken breasts in the center, spacing them apart. Arrange potatoes in one section and scatter vegetables in the remaining space in a single layer.
Roast on the center rack for 20-25 minutes. Begin checking at 20 minutes — chicken is done when an instant-read thermometer reads 165°F (74°C) in the thickest part.
For extra-crispy edges, switch to high broil for the final 3-4 minutes. Watch carefully to prevent burning.
Remove from oven and let chicken rest for 5 minutes before slicing against the grain. Garnish with fresh parsley and serve directly from the pan.