German Potato Noodles (Schupfnudeln) With Brown Butter

Ingredients

• 1 lb russet potatoes, scrubbed and dried
• 1 tsp salt
• ¼ tsp black pepper
• ¼ tsp nutmeg
• ½ cup semolina flour, divided as needed
• 1 cup all-purpose flour, divided as needed
• 1 egg
• 2 Tbsp plus ½ cup unsalted butter, divided
• 1 lb mushrooms (oyster, king and/or cremini), cleaned and sliced
• Salt, to taste
• Large handful sage leaves, washed and dried
• 1 cup gruyere cheese, grated
• ¼ cup parmesan cheese, grated
• 1 lemon, zested
• Pepper, to taste