Cook butter in saucepan over medium heat for 5-8 minutes, stirring often, until butter begins to foam and turn brown.
Transfer butter to mixer bowl. Add egg, brown sugar, vanilla, and salt. Beat at medium speed for about 3 minutes, until mixture falls back on itself in a ribbon.
Add flour and mix until fully incorporated.
Toast macadamia nuts on baking sheet for 4-6 minutes, until golden brown and fragrant. Let cool and chop coarsely.
In mixing bowl, beat brown sugar and butter at medium speed for about 5 minutes, until light and fluffy. Scrape sides occasionally to ensure ingredients are incorporated.
Change speed to low and add one egg at a time, making sure to incorporate each thoroughly before adding next egg.
In another bowl, whisk flour, baking powder, and salt.
Add vanilla and dry ingredients to mixing bowl, again scraping sides occasionally. Fold in half the macadamia nuts.
Butter 13 x 9–in/33 x 23–cm baking dish and lightly dust with flour. Scrape two-thirds of batter into baking dish and smooth with spatula. Evenly distribute half the brown butter mixture on top. Add remaining batter, again smoothing with spatula. Evenly distribute remaining brown butter mixture. Sprinkle remaining macadamia nuts on top.
Bake at 375° F/190° C for 25-30 minutes, until cake edges are golden brown and firm. Cake center will be soft.
Cool to room temperature before serving so cake will set. Garnish with White Chocolate Mousse Whipped Cream.
White Chocolate Mousse Whipped Cream
Mix heavy cream, powdered sugar, and vanilla for 2 minutes.
Add white chocolate mousse powder and continue whipping until stiff peaks are formed. Refrigerate until use.