For cake: In a skillet over medium heat, melt the butter and allow it to cook until the butter turns a deep golden brown color and has a nutty aroma, 5 to 7 minutes, while you occasionally swirl the skillet. Remove from heat and pour into a heatproof bowl. Refrigerate, stirring every 20 minutes, until butter cools to room temperature, 70°F to 72°F (21°C to 22°C).

Preheat the oven to 325°F (160°C). Generously spray a 15-cup Bundt or tube pan with baking spray with flour.

In a large bowl, whisk together cake flour, salt, baking soda, and nutmeg. In a small bowl, whisk together sour cream and milk.

In the bowl of a stand mixer fitted with the paddle attachment, add cooled brown butter and shortening and mix on medium speed for 3 minutes. Then scrape down the sides of the bowl and add the sugar and continue to mix for 2 minutes.

Begin adding the eggs, one at a time, ensuring that each egg is fully incorporated prior to adding the next. After the second egg is added, scrape down the sides of the bowl again and continue to add two more eggs. Scrape down the sides of the bowl again after the 4th eggs and again after the 6th egg is added.

Add in the emulsions or extracts and mix until fluffy and smooth, for 1 to 2 minutes.

Add half of the dry ingredients, and mix until combined. Then add the sour cream and milk mixture and mix until fully incorporated. Add the remainder of the flour mixture and mix until combined, about 20 seconds. Scrape down the sides of the bowl, and mix until the batter is smooth, 10 to 15 seconds.

Pour the cake batter into the pan, and smooth the batter into an even layer.

Bake until golden brown and a wooden pick inserted near center comes out clean, 1 hour and 10 minutes to 1 hour and 30 minutes.

For glaze: While the cake is baking, add butter to a saucepan over medium heat and cook until browned. Add sugar and ¼ cup (60 grams) water, and stir until the sugar is dissolved, then stir in the emulsion or extract.

Once the cake is finished baking, prick holes in the top of the cake with a wooden pick or skewer while it's still hot in the pan. Slowly pour half of the butter glaze all over the top. Allow it to cool in the pan for 10 minutes. Then turn the cake out of the pan onto a wire rack, and use a pastry brush to gently brush the entire cake with the remaining glaze. Let the cake cool completely. Store in an airtight container for up to 5 days.