2 pounds sweet potatoes, peeled and cut into 1-inch pieces
1 pound Yukon gold potatoes, peeled and cut into 1-inch pieces
1 stick unsalted butter, plus 1 ounce (2 tablespoons), melted
2 1/2 tablespoons chopped fresh sage
1 1/2 cups milk, warmed
Coarse salt and freshly ground pepper
1 cup fresh breadcrumbs (from 3 slices white bread, crusts removed)
Place sweet potatoes and potatoes in a large saucepan; cover with water, and season with salt. Bring to a boil; reduce heat, and simmer until potatoes are tender, about 9 minutes. Drain; pass through a ricer into a bowl.
Preheat oven to 375 degrees. Melt 1 stick butter in a small saucepan over medium heat, swirling occasionally, until golden brown, 5 to 7 minutes. Remove from heat; add 2 tablespoons sage. Stir butter mixture and milk into potatoes. Season with salt and pepper. Transfer to a 2-quart casserole dish. (Mixture can be refrigerated for up to 2 days.)
Combine breadcrumbs with 2 tablespoons melted butter and remaining 1/2 tablespoon sage. Season with salt and pepper. Toss to combine.
Top potato mixture with breadcrumbs. Bake, uncovered, until bubbling around edges and breadcrumbs are golden brown, 30 to 40 minutes. (If browning too quickly, tent with foil.) Let stand, uncovered, for 10 minutes.
The potato puree can be refrigerated for up to two days. Make the breadcrumbs and sprinkle them on top just before baking. (The dish may need to bake for 10 to 15 minutes longer if cold.)