Preheat oven to 300°F. Line baking sheet with lightly oiled foil.
Rub insides of squash with olive oil and sprinkle lightly with salt. Place squash cut-side down on baking sheet with two sage leaves and one garlic clove under each half. Roast squash for 45 minutes to an hour, or until you can squeeze squash and it is soft. Cool.
While squash cools, heat milk. Scoop flesh out of squash. Put through food mill into heavy-bottomed pot. Add three ounces of butter and heat squash to incorporate butter. Stir in warm milk, starting with one-and-a-half cups and continuing until desired consistency of purée is reached. Season to taste with salt and pepper and spoon into serving dish.
Put remaining butter and sage leaves in heavy-bottomed saucepan. Over medium heat, slowly melt butter, swirling constantly until foam subsides, color starts to turn brown, and butter has nutty aroma. Immediately pour browned butter over squash, as it will quickly burn if left in hot pan.