Preheat oven to 400°F (205°C). Toss the potatoes in with 2 tbsp vegetable oil in a large bowl and season liberally with salt and pepper. Spread the potatoes evenly across the bottom of an 8-by-12-inch baking pan.
Add parsnip slices into the bowl used to season the potatoes and toss. Add up to an additional tbsp vegetable oil if needed to coat the parsnips.
Place parsnip slices on top of the potatoes and season with paprika. Bake for 35 minutes or until tender.
While the parsnips are cooking, wilt the spinach. Put 1/2 inch water in a large, wide pot over high heat. When water boils, add minced garlic. Add spinach to the pot. Season lightly with salt and pepper, then twirl with tongs to barely wilt the spinach, about a minute or less. Remove spinach from pot and cool.
Once the potatoes are done, remove them from the oven. Remove the parsnips with a pair of tongs and spread the wilted spinach across the center of the ban. Place the parsnips atop the spinach for serving. Garnish with fresh dill if desired.