1. Bring broth and water to a simmer in a saucepan.
2. Heat 1 tablespoon oil in a nonstick skillet over medium-high heat. Cook squash with 1/2 teaspoon salt and 1/4 teaspoon pepper, stirring occasionally, until it is golden in spots (8-10 minutes). Stir in thyme. Add 1/2 cup broth mixture to skillet, reduce heat and cook, stirring occasionally, until squash is tender and broth is evaporated (8 to 10 minutes more). Remove from heat and set aside.
3. Meanwhile, in a 4-quart heavy pot over medium heat, cook onion in remaining 1 1/2 tablespoons oil with remaining 1/2 teaspoon salt, stirring, until softened (about 6 minutes). Add rice and toss to coat with oil; cook 2 minutes. Add wine and cook until almost completely absorbed (2 minutes more).
4. Stir 1/2 cup simmering broth into rice and cook at a strong simmer, stirring frequently, until broth is absorbed. Continue simmering and adding broth 1/2 cup at a time, stirring constantly and letting each addition be absorbed before adding more, until rice is creamy-looking but still al dente (about 20 minutes total); mixture should be the consistency of thick soup. (There may be leftover broth.)
5. Stir in butter, cheese, and reserved squash. Serve immediately.