Preheat your oven to 350°F (make sure the rack is in the center). In a large mixing bowl, add the flour, salt, baking soda, baking powder, ground cinnamon, and ground ginger.
Whisk everything together for about 30 seconds to evenly distribute the leavening and spices (this simple step guarantees no spicy bites or flat spots!). Set the bowl aside while you finish the wet ingredients.
Take the bowl of brown butter out of the freezer—it should now be opaque and have the soft, creamy texture of whipped or softened butter. Give it one final vigorous stir to make sure it’s perfectly smooth and spreadable, then set it aside.
In the bowl of a stand mixer (or a large mixing bowl with a hand mixer), add the sugar, unsalted butter, and the chilled brown butter.
Beat on medium speed for 2–3 minutes, scraping down the sides as needed, until the mixture is light, fluffy, and a gorgeous pale golden color.
With the mixer on medium speed, add the eggs one at a time—beat well after each addition (about 20–30 seconds) until fully incorporated and the mixture looks smooth and glossy. Scrape down the sides of the bowl as needed so everything blends evenly
.Finally, pour in the pure vanilla extract and mix for another 10–15 seconds. That gorgeous speckled batter is now silky, fragrant, and ready for the dry ingredients.
With your mixer on low speed (to avoid a flour cloud!), add the dry ingredients and milk to the butter egg mixture in alternating additions. Scrape down the bowl once or twice to make sure everything is beautifully combined.
Carefully pour the warm pears and the caramel-brown butter sauce into your prepared springform pan. Use a rubber spatula to gently spread the pears and sauce into an even layer across the entire bottom. Arrange the pear slices in overlapping circles (start from the outside and work your way in, with the thin ends pointing toward the center).
Gently dollop the thick brown butter cake batter over the arranged pears (dropping it in big spoonfuls prevents disturbing your pretty pear design)
Using an offset spatula or the back of a spoon, carefully spread the batter into an even layer, completely covering the pears and pushing it right to the edges of the pan.
Slide the pan into your preheated 350°F oven and bake for 25–30 minutes, until the top is golden brown and a toothpick inserted in the center comes out almost clean with just a few moist crumbs clinging to it (no wet batter!).
As soon as the cake comes out of the oven, set a timer for 1–2 minutes only — just long enough to let it settle, but still warm enough for an easy release.
Run a thin, sharp knife (or offset spatula) around the inside edge of the pan to free any stuck spots.
Place your serving plate or cake stand upside-down on top of the pan. Using both hands (and oven mitts!), confidently flip the whole thing in one smooth motion. Give the pan bottom a gentle tap or two if needed.
Immediately unlatch and remove the springform ring. Carefully slide the metal base upward off the cake, then gently peel away the parchment paper to reveal those stunning caramelized pears in all their glossy glory.
Let the cake cool completely (or at least to room temperature) so the pear topping sets beautifully.
Right before serving, place a fine-mesh sieve or powdered sugar duster over the cake and generously shower it with powdered sugar — it’ll settle into all the pear crevices like fresh fallen snow and add that perfect sweet, elegant touch.
Slice into 8 wedges (a sharp knife wiped clean between cuts gives the prettiest slices), plate, and give each piece one last loving dusting of powdered sugar.Serve immediately.