Candy the pecans: Preheat oven to 400 degrees. Toss toasted pecans with butter, brown sugar, vanilla, cinnamon, and nutmeg on a rimmed baking sheet. Roast, stirring to coat halfway through, until toasted, about 10 minutes. Let cool.
Reduce oven temperature to 350 degrees. Make the cake: Butter three 8-inch round cake pans, and dust with flour, tapping out excess. Sift flour, baking powder, and 1/2 teaspoon salt into a bowl. Beat butter and 1 1/4 cups granulated sugar with a mixer on medium speed until pale and fluffy, about 3 minutes. Add flour mixture in 3 additions, alternating with milk, beginning and ending with flour. Stir in candied pecans.
Beat egg whites in a clean bowl with a mixer on high speed until frothy. Gradually add remaining 1/2 cup sugar, and beat until stiff peaks form. Gently fold one-third of the egg whites into the batter using a rubber spatula. Fold in remaining egg whites in 2 additions.
Divide batter among pans. Bake until cakes are set and a toothpick inserted into the center of each comes out clean, about 30 minutes. Let cool on a wire rack for 10 minutes. Turn out cakes onto racks, and let cool completely.
Meanwhile, make the pear filling: Brown butter in a skillet over medium heat, about 5 minutes. Cook pears, stirring occasionally, until tender, about 6 minutes.
Make the bourbon whipped cream: Whisk cream, bourbon, and confectioners' sugar with a mixer on medium-high speed until soft peaks form.
Trim tops of cakes to create a level surface using a serrated knife. Transfer 1 cake to a platter. Spread half the pears over the top. Top with another cake. Spread remaining pears over the top. Top with remaining cake. Spread whipped cream over the top. Garnish with chopped pecans.
Layered cake can be refrigerated for up to 3 days. Top with whipped cream just before serving.