Toss the butternut squash cubes with 2 tablespoons of the olive oil and spread on a parchment-lined baking sheet in a single layer. Season with salt and black pepper. Roast for 30-40 minutes, or until tender. Remove from the oven and set aside.
Meanwhile, bring a large pot of salted water to a boil. Cook pasta according to package directions or desired tenderness. Drain and set aside, reserving ½ cup of cooking water.
While the pasta cooks, heat the remaining olive oil in a nonstick skillet over medium-high heat until shimmering. Add the vegetarian bacon to the pan and saute for 5-6 minutes, or until crispy, stirring occasionally. Stir in the garlic and sauté until fragrant, another 30 seconds. Remove from the heat.
In a medium bowl, whisk together the eggs and parmesan cheese. Slowly add the egg mixture to the hot pasta, stirring constantly so that the eggs will cook but not scramble. Add in cooking water as needed to reach a sauce of desired consistency. Stir in the butternut squash cubes and the bacon-garlic mixture. Season to taste with salt and black pepper. Serve warm.
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