Preheat oven to 400 degrees Fahrenheit. Line a baking tray with parchment paper and arrange the 3 cups finely diced butternut squash on the tray.
Drizzle with enough oil to lightly coat the butternut squash, toss. Sprinkle generously with salt and pepper to taste. Place into the oven for 15 minutes, toss, and cook until lightly golden and tender. Remove from oven.
Cook the pasta in salted water until just al dente and drain, but reserve ½ cup of the pasta cooking water.
Meanwhile, cut the florets from the romanesco stem and cut into small florets.
In a large pan, add 1 tbsp. of the olive oil on medium heat. Once hot, add the romanesco and saute for a few minutes, then add the sage leaves and cook until the romanesco is starting to lightly brown and become tender. Transfer romanesco and sage to a plate.
Add the remaining olive oil and 1 tbsp. vegan butter to the pan with the finely chopped onion and saute for around 8 minutes until translucent. Stir and add a bit of water during cooking to prevent burning if needed.
Add the 4 minced garlic cloves to the onions, cook another minute. Add the ¼ cup vegetable broth, and simmer until the liquid has reduced by half.
Meanwhile, add the 2 tbsp. vegan butter to a separate small pan, along with the 1/3 cup breadcrumbs. Cook over medium heat, as the butter melts and breadcrumbs turn golden brown, stirring occasionally. Remove from heat and set aside.
Add the butternut squash, pasta, and romanesco to the large pan with the onions and garlic. Stir, and add ¼ cup of the pasta cooking water along with a drizzle of olive oil, juice of 1/2 lemon, and most of the 1/3 cup fresh parsley, toss. Serve and top with the breadcrumbs and the remaining fresh parsley.