Heat a large sauté pan over medium heat. Add the butter. Once the butter has melted, add the apples. Season with a pinch of salt. Let the apple sauté until soft and caramelized.
Add the maple syrup and bring to a simmer. Lower the heat and simmer for 2 minutes. Turn the heat off and set aside. Let cool slightly.
Preheat the oven to 350°F. Line a 9” cake pan with a piece of lightly oiled parchment paper. Add the butter to a sauté pan and let it melt over medium-high heat. Continue to cook until the butter browns slightly and smells nutty. Let cool.
Combine the flour, sugar, baking powder, and salt together in a mixing bowl. Whisk until incorporated. In a separate bowl, crack and beat the eggs. Whisk in the ricotta cheese, brown butter (from above), and vanilla extract.
In two batches, fold the dry ingredients into the wet ingredients until smooth (don’t overmix). Lastly, fold in ¾ of the maple apples. Pour the batter into the prepared pan and smooth out the top. Arrange the remaining maple apples across the cake, gently pressing them into the batter.
Bake the cake for about 45-50 minutes, or until just cooked through. Remove the pan from the oven and let the cake cool for 10 minutes. After 10 minutes, lift the parchment paper to retrieve the cake.
Cut into slices. Serve warm or at room temperature with a sprinkle of raw sugar and a drizzle of warm maple syrup.