STEP 1 Put a large pot of water on to boil.
STEP 2 Using a spiral vegetable slicer or julienne vegetable peeler, cut sweet potatoes lengthwise into long, thin strands. You should have about 12 cups of “noodles.”
STEP 3 Cook the sweet potatoes in the boiling water, gently stirring once or twice, until just starting to soften but not completely tender, 1 1/2 to 3 minutes. Reserve 1/4 cup of the cooking water, then drain. Return the noodles to the pot, off the heat. Combine eggs, Parmesan, salt, pepper and the reserved water in a bowl; pour over the noodles and gently toss with tongs until evenly coated.
STEP 4 Heat oil in a large skillet over medium heat. Add bacon and mushrooms and cook, stirring often, until the liquid has evaporated and the mushrooms are starting to brown, 6 to 8 minutes. Add garlic and cook, stirring, until fragrant, about 1 minute. Add spinach and cook, stirring, until wilted, 1 to 2 minutes. Add the vegetables to the noodles and toss to combine. Top with a generous grinding of pepper.