Preheat oven to 400°F. Line a rimmed baking sheet with foil or parchment paper; spray with nonstick cooking spray.
On the prepared pan, toss together the potatoes, carrots, shallots, garlic, thyme, rosemary, 2 tablespoons of olive oil, 1 teaspoon of kosher salt, and ¼ teaspoon of ground black pepper. Spread in a single layer.
Bake for 20 minutes. Stir the potatoes and carrots. In a large bowl, toss together the broccoli, 1 tablespoon of olive oil, ½ teaspoon of salt, and a little bit of ground black pepper. Spread the broccoli on the pan with the potatoes and carrots. Bake for about 15-20 more minutes, or until the vegetables are golden brown and tender. Stir the vegetables. Leave the oven on.
In the same bowl that you used for the broccoli, toss together the shrimp, the remaining 1 tablespoon of olive oil, and the Old Bay seasoning. Arrange the shrimp on the pan with the vegetables. Bake until the shrimp are pink and firm, about 6-8 minutes. Discard the herb stems, garnish with fresh herbs, and serve.