Heat oven to 425°F. Cut squash into 3/4-inch cubes. Toss with 1 tablespoon oil, 1/4 teaspoon salt, and pepper as desired. Spread out on a nonstick baking sheet and roast, stirring at 30-min mark, until golden brown all over, about 45 minutes.
Tear kale leaves into smaller pieces. Combine in a food processor with garlic, almonds, Parmesan, and 1/2 cup plus 2 tablespoons oil. Process until smooth, periodically scraping sides of the bowl if necessary.
Cook pasta in boiling water. Drain when ready, but reserve 1/2 cup of the water.
Toss pasta in a large skillet with 1/2 cup pesto, the pasta water, and remaining 1/2 teaspoon salt, plus pepper to taste. (Reserve remaining pesto for another use.) Cook over medium-high heat, tossing, until very hot and liquid thickens and coats the pasta, about 2 minutes.
Divide among 4 bowls and top with roasted squash. Sprinkle with more Parmesan and serve.
