In a saucepan over high heat, bring turkey or chicken stock to a boil. Reduce heat to low and bring to a simmer.
In a separate saucepan over medium-high heat, melt butter and cook onions for 5 minutes, or until translucent. Add rice and stir well to coat. Cook, stirring often, for 3 minutes, being careful not to brown rice or onions.
Add 1-1/2 cups hot stock to rice mixture and stir until most of the liquid is absorbed. Add another 1 cup hot stock and stir until most of the liquid is absorbed. Repeat with another 1 cup hot stock until rice is barely al dente.
Add squash and remaining stock. Cook for 1 minute. Add cheese and stir until well incorporated.