Preheat the oven to 425ºF and line a baking sheet with parchment paper. Trim and slice delicate squash lengthwise, then deseed and slice in ¼-inch crescents. Thinly slice fennel bulb, reserving fronds for the salad. Lay squash crescents and fennel on the parchment in a single layer, and drizzle with olive oil. Toss to coat evenly, then sprinkle with salt and pepper. Roast for 30 minutes, flipping halfway through. Remove and set aside to cool.
Reduce heat to 350ºF.
In a large bowl, whisk eggs, sour cream, salt, and pepper until completely homogenous. Stir in ¾ cup of the grated parmesan cheese.
Place 1 tablespoon of olive oil in a 12-inch cast iron skillet or other ovenproof frying pan, and swirl to coat bottom and sides. Add ¼ cup minced shallot and sauté over medium heat until tender and beginning to brown.
Transfer the roasted squash and fennel to the pan. Pour in the egg mixture, and cook the frittata over medium heat, without stirring, until its edges begin to set, about 5 minutes. Sprinkle the top with the remaining ¼ cup of parmesan cheese and transfer skillet to oven.
Bake the frittata until it’s puffy and golden brown and the center is set, 22-25 minutes.
While the frittata bakes, toss the arugula, fennel frond, and dill in a medium bowl. Whisk together the dressing ingredients in a small bowl, and toss the salad, with dressing to taste, just before serving.