Preheat the oven to 375 degrees F.
For the Parmesan Frico Cups:
Place a silpat mat on a baking sheet. Place 6 (1/4-cup) mounds of Parmesan cheese on the mat and gently tap down until each mound is flat and 4 1/2 to 5 inches in diameter. Bake for 8 to 10 minutes, until golden and bubbly. Working quickly, use a thin spatula to transfer the Parmesan Frico to a muffin tin. Gently place a small drinking glass on top of the Parmesan Frico to mold it into the shape 1 of the muffin cups. Let cool until firm, about 5 minutes. Continue with the remaining Parmesan cheese.
For the Citrus Vinaigrette:
Combine all the ingredients in a jar or a tight-sealing plastic container. Shake to blend.
For the Spinach Salad:
In a large bowl, combine all the ingredients. Drizzle with vinaigrette and toss to combine. Divide the salad among the Parmesan Frico Cups and serve immediately.