Add 12 cups water to a large pot. Once boiling, add 1 tablespoon salt and the potatoes. Cook until a fork easily pierces them (20-25 minutes for small potatoes, around 30 minutes for larger ones).
Heat oven to 400°F.
In a bowl, combine the basil, parsley, oregano, garlic powder, onion powder, thyme, salt (½ teaspoon), and pepper (⅛ teaspoon). Set aside 2 teaspoons of this mixture. In a separate bowl, mix the remaining seasoning with minced garlic and melted butter until smooth.
Drain potatoes and let stand to dry, about 5 minutes. Place potatoes on a clean surface. Working with one potato at a time, cover with a clean kitchen towel. Apply pressure with your palm on top of the towel and potato. Smash the potato to the height of ½-inch and remove the towel. Use a metal spatula to gently scrape up the potato and transfer to one side of the sheet pan. Repeat until all potatoes are smashed and on the pan.
Use a pastry brush to evenly coat the potatoes with the garlic-butter mixture. Drizzle 1 tablespoon oil over the potatoes.
On the other half of the sheet pan, add the sausage, broccoli, and bell pepper. Toss with remaining 2-½ tablespoons olive oil and the reserved 2 teaspoons seasoning until well coated.
Bake for 25-30 minutes, until the veggies are tender and the potatoes are crispy. For extra crispiness, broil on high for 2-3 minutes, watching closely.
Grate Parmesan cheese over the hot potatoes, if desired. Serve with the optional Dijon sauce.
Juice ½ of a lemon to get 1 tablespoon juice. Whisk together Dijon mustard, mayonnaise, and lemon juice. Season with salt and pepper to taste.