Heat 2 tablespoons oil in heavy large pot over medium-high heat. Add squash and sauté until beginning to soften and brown around edges, about 5 minutes. Transfer squash to medium bowl.
Reduce heat to medium; add remaining 1 tablespoon oil, leeks, and thyme to same pot and stir until tender but not brown, about 5 minutes. Add rice and stir 1 minute. Add 1 cup broth and simmer until absorbed, stirring frequently, 3 to 4 minutes. Add remaining broth by 1/2 cupfuls, allowing each addition to be absorbed before adding next, stirring often, about 15 minutes.
Return squash to pot. Continue to cook until rice is just tender but still very creamy, stirring gently and often, about 10 minutes longer (about 25 minutes total cooking time). Remove from heat. Stir in basil and 3/4 cup freshly grated Parmesan cheese. Season to taste with salt and pepper. Transfer to large bowl and serve with additional Parmesan cheese.