To make the dressing, combine all dressing ingredients other than olive oil in a small bowl.
Use a small whisk and, whisking constantly, drizzle olive oil into the mixture slowly to combine.
Preheat oven to 400, and put a metal sheet pan in the oven while it preheats.
When oven is preheated, remove sheet pan and arrange the brussels sprouts and delicata slices on the pan. Drizzle with 2 tbsp. olive oil and season with salt and pepper. Return to the oven and roast for about 25 minutes, using a spatula to stir the vegetables once or twice mid-roast.
While vegetables are roasting, arrange greens on four plates.
Heat 1 tbsp olive oil in a 12 inch skillet over medium heat. Add prosciutto slices and fry until crisp, about 1 minute per side. Remove prosciutto to a paper towel to cool, leaving drippings in the skillet.
Add remaining 3 tbsp olive oil to the skillet and increase heat to medium high. Add scallops and sear them until brown on each side and opaque through the middle, 1-2 minutes per side. Remove seared scallops to a plate and take pan off the heat.
Arrange roasted vegetables atop the greens on each plate. Add half of the prepared dressing to the skillet while it's still hot, and use a spatula to scrape up any crispy bits of scallop or prosciutto left in the pan. Then pour off skillet contents back into your dressing bowl to recombine with remaining dressing.
Arrange scallops on top of the four salads. Drizzle dressing over all. Finally, crumble a slice of prosciutto into bits over each salad.
Serve immediately while scallops and veggies are still warm!