Place bread crumbs and flour onto 2 separate plates. Place beaten egg in a small bowl. Divide goat cheese in 1/2 and roll into two balls. Flatten the balls to 1/2-inch thickness.

Coat both cheese medallions with flour; dip into beaten egg. Coat evenly with bread crumbs. Spoon chopped pistachios on top of each, gently pressing into cheese. Place in a baking dish, cover, and refrigerate at least 30 minutes.

Preheat the oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper.

Cut beet and sweet potato into spirals using a spiralizer. Remove stem, seeds, and ribs from peppers; cut into rings. Spread out vegetables on the prepared baking sheet. Drizzle with 1 tablespoon olive oil. Remove cheese medallions from the refrigerator and make space for them on the baking sheet.

Bake in the preheated oven until vegetables have softened and cheese medallions have slightly browned, about 10 minutes. Let cool for 5 minutes on the baking sheet.

While cheese and vegetables are cooling, combine 1/4 cup olive oil, shallot, shelled pistachios, flat-leaf parsley, vinegar, honey, and Dijon mustard in a food processor. Puree on high until the mixture is completely liquefied, 1 to 2 minutes. Season vinaigrette with salt and pepper to taste.

Divide spinach between 2 plates. Top with beet and sweet potato spirals, sweet pepper rings, and a cheese medallion. Drizzle vinaigrette on top and serve immediately.