First, brown the butter. Cut the 4 tablespoons of butter into pieces and add to a small skillet. Heat on medium until it melts , then continue to heat and stir as it starts to foam, then bubble and crackle, and finally quiet down and the bottom will get dark quickly. Pull before it burns! I have a post on how to brown butter if you need more info. Set aside.
Dice your peaches and add to a medium bowl. Add the spices, 3 tablespoons of brown sugar, vanilla, almond extract, and lemon juice, and stir together.
Let sit for 10 minutes or so (you can make the topping while it sits). Then add the bourbon and the cornstarch and stir everything together.
To make the topping, add the browned butter, 1/2 cup of brown sugar, flour, oats, salt, and cinnamon to a small bowl. Use a fork to stir together so everything is moistened.
Pour the peach mixture into a baking dish (mine was an odd size, but just choose one big enough for your filling to be decently thick). Cover fully with the topping mixture.
Bake for 30 to 45 minutes...it will very much depend on the thickness of your filling and topping, but you want the filling to be bubbling up around the sides and the topping to get golden and smell amazing. Let sit for at least 10 minutes (more like 30 is ideal) to let the juices thicken and set.