In a large, wide skillet, cover squash and 1 tsp. salt with water. Bring to a simmer over high heat. Reduce heat to medium-low and simmer until tender, 4 to 5 minutes. Remove from heat; drain squash.

In the same skillet over medium heat, melt 2 Tbsp. butter. Add onion; season with 1/2 tsp. salt. Cook, stirring occasionally, until onion is translucent, 7 to 9 minutes. Add garlic and sage and cook, stirring, until fragrant, about 1 minute more.

Add orzo and remaining 2 Tbsp. butter and cook, stirring occasionally, until toasty and golden brown, 2 to 3 minutes. Add 1/2 tsp. salt and 2 2/3 cups water, then bring to a simmer over medium-high heat. Reduce heat to medium-low; cover and simmer until orzo is tender and liquid is absorbed, 7 to 8 minutes.

Meanwhile, reserve 1 cup cooked squash. Transfer remaining squash to a blender. Add 3 Tbsp. water and blend until smooth.

Add pureed squash to orzo mixture and stir until creamy and combined. Fold in Parmesan, 1/4 tsp. pepper, and reserved squash and cook, stirring, until cheese is melted and squash is heated through, about 3 minutes; season with salt, if needed.

Divide orzo mixture among bowls. Top with more Parmesan and pepper.