1. Preheat the oven to 400 degrees F.  Adjust the oven rack to the middle position. Cover a large baking sheet with parchment paper, and brush lightly with olive oil (to prevent sticking).
2. Working in a large baking dish or sheet pan, toss the carrots with the olive oil. Combine the paprika, garlic powder, and Italian seasoning and toss with the carrots, getting them nice and coated. Season with salt and pepper. You can adjust these seasonings to suit your taste, by the way. 
3. Sprinkle the shredded fontina all over the prepared baking sheet. Put the grated parmesan on a plate. Dip/coat the cut side of each carrot in the grated parmesan, creating a thick crust, and lay them all side by side on top of the shredded fontina, you want them almost touching.
4. Roast the carrots until golden brown and the cheese is melty and visibly browned, about 20 to 25 minutes. Allow them to cool for several minutes before transferring them to a serving plate/platter, as the cheese will firm and crisp up as it cools. Serve with the salsa verde for drizzling or dipping. 

For the Salsa Verde

1. Combine the parsley, basil, capers, anchovies, vinegar, garlic, and olive oil in a blender, and season with a little salt and pepper. If your carrots had tops, use those here! Blend until mostly smooth, adding more oil if needed to get things moving. Transfer to a small bowl to serve.