Fill a large pot with one inch of water and bring it to a simmer. In a medium stainless steel bowl, combine strawberries, lemon zest, and ΒΌ cup of sugar. Cover with plastic wrap and place the bowl on the pot of simmering water (the water should not be touching the bottom of the bowl). Let strawberries cook for 20 minutes.
Remove the bowl from the pot; refrigerate until chilled (may be made one day ahead).
In a small saucepan, melt the butter over medium-high heat. Simmer, whisking constantly, until the butter is a golden-amber color and smells nutty, about 4 to 6 minutes (you'll begin to see browned bits floating in the bottom of the pan). Reduce heat if it's boiling too rapidly. Watch the butter closely as it turns from browned to burnt rather quickly. Remove from heat and let cool.
Preheat the oven to 350 degrees F. Place a 9 or 10-inch cake pan on parchment paper, trace a circle, and cut out. Spray the pan with nonstick spray, then place the round piece of parchment into the bottom of the pan and spray one more time. Sprinkle a couple of spoonfuls of flour into the pan, tap and coat the bottom and sides of the pan, and discard any excess flour.
In a large bowl, whisk eggs and 1 cup of sugar vigorously for about 2 minutes. The mixture will be bright yellow. Set whisk aside and use an electric mixer to whip the eggs & sugar on high speed until the mixture is thick and paled in color (2 to 3 minutes more). Reduce speed to low and slowly add in the cooled brown butter. Make sure you scrape in all of the brown bits too.
Sift flour, baking powder, and salt together. Using a whisk, gently stir in one-third of dry ingredients into the batter, then half of the buttermilk. Repeat, ending with the last third of the dry mixture. Scrape the batter into your prepared pan.
Bake until the cake sides pull away from the pan and a toothpick inserted into the center comes out clean, about 25 minutes for a 10-inch pan and about 40 minutes for a 9-inch pan. If the cake appears to be browning too quickly, cover lightly with foil in the last 10 minutes of baking.
Let the cake cool on a wire rack for about 20 minutes before removing from the pan. Run a knife around the edge of the pan and invert it onto a wire rack to cool completely.
Cut wedges and serve topped with strawberry sauce (or simply sliced fresh strawberries) and whipped cream.
