Brown the Butter and Infuse with Sage
In a medium saucepan, melt the butter over medium heat.Continue cooking, stirring occasionally, as the butter foams and then begins to turn golden brown—about 8-10 minutes. Watch carefully, as it can burn quickly!
When the butter develops a nutty aroma and amber color with little brown bits at the bottom, remove from heat.
Add 1 tablespoon of the chopped sage to the hot brown butter and let it steep for 5 minutes. The residual heat will extract the sage's aromatic oils.
Set aside ¼ cup of this sage-infused brown butter for the apple filling.
Prepare the Apple Filling
Preheat your oven to 350°F (175°C).In a large bowl, combine the sliced apples, granulated sugar, lemon juice, cinnamon, nutmeg, cloves, and cornstarch.
Pour in the reserved ¼ cup of sage-infused brown butter and add the remaining 1 tablespoon of chopped sage and the vanilla extract.
Toss gently until all apple slices are evenly coated.
Make the Brown Butter Crumble Topping
In a medium bowl, combine the flour, oats, brown sugar, salt, and remaining tablespoon of chopped sage.Pour in the remaining brown butter (should be slightly cooled but still liquid).
Mix until the mixture forms coarse crumbs. If using nuts, fold them in now.
Assemble and Bake
Transfer the apple mixture to a 9×13-inch baking dish, spreading it evenly.Sprinkle the crumble topping uniformly over the apples, covering the entire surface.
Bake for 45-50 minutes, until the topping is golden brown and the apple filling is bubbling at the edges.
Let cool for at least 15 minutes before serving.