In 3-quart saucepan, cover potatoes and squash with water; add 1 teaspoon salt. Bring to boil over high heat; reduce heat, cover, and cook until tender, 12–15 minutes.
In small saucepan over medium heat, mix 2 tablespoons butter and sage. Tilting pan and watching closely, cook about 3 minutes, until butter foams and begins to brown; keep warm.
Thoroughly drain potatoes and squash, return to pan and shake 1–2 minutes over low heat.
Using a hand masher, roughly mash to create chunky mixture.
Over low heat, gently mix in remaining butter and milk. Season with salt and pepper, to taste.
Spoon into serving bowl and drizzle with brown butter and sage.