To make the loaf:

1. Add the entire 1/2 cup of unsalted butter to a steel or light colored saucepan. Try to use one with a heavier bottom to prevent the butter from burning.
2. Melt the butter over medium heat and continue to cook. The butter will sizzle and foam a bit before the milk solids sink to the bottom. Once they do, you’ll be left with the clear golden butterfat on top and a good view of the milk solids on the bottom of the pan.
3. Watch the milk solids closely, stirring occasionally as they continue to cook. Eventually, they’ll begin turning a light golden and the butter will smell fragrant and nutty. Stir the browning butter constantly for barely another 10 seconds or so, and pull it from the heat as soon as it becomes a medium toasty brown.
4. Immediately pour the browned butter into a heatproof glass measuring cup (I use Pyrex) and allow it to cool for 30 minutes before continuing the recipe. Alternatively, you can place the cup in the freezer for 15 minutes, but be sure to use a hot pad underneath the cup. Preheat the oven to 350 once you’ve finished browning the butter.
5. Once the butter has cooled a bit, set it aside and whisk the flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg and cloves together in a small mixing bowl. Set the dry ingredients aside.
6. In another, larger mixing bowl, add half of the browned butter (1/4 cup liquid), the pumpkin puree, granulated sugar, brown sugar, ricotta cheese, oil, egg, egg yolk and vanilla extract. Whisk the wet ingredients together well until blended and smooth. Set the remaining 1/4 cup of browned butter aside for the frosting.
7. Add the dry ingredients to the wet all at once, and gently fold the batter together with a spatula. The batter will be quite thick, but still slightly pourable.
8. Lightly grease or line a 9 x 5 loaf pan with parchment paper and scrape the batter into the pan. Use an offset spatula or butter knife to smooth out the surface. Bake the loaf at 350 for 45 minutes, or until the top springs back lightly when pressed with your finger.
9. Allow the loaf to cool for 15 minutes in the pan, then turn it out onto a cooling rack to finish cooling to room temperature. Be sure that the loaf is fully cooled before frosting, or the frosting will melt and get messy.

Make the frosting:

1. In a large mixing bowl, beat the cream cheese on medium speed until it’s smooth and creamy. Add the remaining 1/4 cup browned butter, powdered sugar, heavy cream, cinnamon, salt and vanilla extract (or bean paste.)
2. Beat on medium speed for another minute. The powdered sugar will cause the cream cheese to release a little moisture, so the frosting will end up a little more loose than you think. This is okay! The consistency will be nice and spreadable, but it will still set up into a perfect thick icing.
3. Frost the cooled loaf with the entire batch of icing. It will be quite a thick layer on top. Allow the frosted loaf to set in the fridge for a couple hours to completely chill and to allow the frosting to set up.
4. Cut into slices and serve. Leftovers may be refrigerated for a few weeks or stored at room temperature for 3 days.