Preheat oven to 400°F. Separate the oven racks to allow two baking sheets to cook at the same time. Line 2 large baking sheets with parchment paper or a silpat and set aside.
To spiralize the Butternut Squash: Slice the neck off a large butternut squash making a straight cut. Peel the outside of the squash neck and slice the stem off making flat/straight cut. Place the large end of the neck on the blade side of your spiralizer and using the 1/8 inch or 3mm blade, and spiralize into noodles (it will yield 4-5 cups).
Place the noodles in a large mixing bowl, toss with 2 teaspoons of olive oil and spread on one of the prepared cooking sheets. Set aside.
In a small bowl, whisk together the 2 tablespoons of olive oil and balsamic vinegar.
Add the Romanesco florets to a large mixing bowl. Drizzle approximately half of the oil and vinegar over the florets and toss to coat. Spoon the Romanesco onto half of the second prepared baking sheet. Sprinkle with a third of the kosher salt (2/3 teaspoon) and bake for 10 minutes.
While the Romanesco is roasting, place the tomatoes in the same mixing bowl used for coating the Romanesco with oil and vinegar. Drizzle with half of the remaining olive oil and vinegar; toss to coat. When the Romanesco has roasted for 10 minutes, remove the tray from the oven and add the coated tomatoes to the same pan; sprinkle with half the remaining salt and return to the oven for 10 additional minutes.
While the other vegetables are roasting, add the asparagus to the same mixing bowl used to coat Romanesco and tomatoes; drizzle with the remaining olive and vinegar, add to the baking sheet with the other vegetables, sprinkle with the remaining salt and cook for 5 minutes.
After 5 minutes, add the baking sheet of butternut squash noodles to the oven and allow both baking sheets to cook 5 more minutes and remove from the oven. Allow to sit for 2 minutes.
Combine the butternut squash, Romanesco, asparagus in a large mixing or serving bowl. Gently toss to mix together. Add the goat cheese and dill; toss again. Lastly add the tomatoes and very gently stir of toss to incorporate them (they will be very soft). Salt and pepper to taste and serve in one large bowl or as individual servings if for a main dish.