Heat oven to 350 F. Grease and line an 8 x 8 inch square pan with parchment paper. Don't skip this step if you actually want to be able to remove your cake from the pan in one piece. Remember, you're not flipping this cake over at the end, so it has to come out of the pan easily. Put butter in a small saucepan and stir over medium heat until golden brown. Watch carefully so that it doesn't burn! This should take roughly 5-8 minutes. Cool slightly.
In a medium bowl, whisk together flour, baking powder, cinnamon and salt; set aside.
In a large mixing bowl, whisk together brown sugar, eggs, and vanilla. Pour the browned butter into the egg mixture, whisking constantly until well blended.
Toss the pears in with the dry ingredients to coat. Stir the pears and dry ingredients into the wet ingredients until combined.
Use a rubber spatula to scrape the cake batter into the prepared cake pan. Smooth the top with a rubber spatula.
Sprinkle the reserved streusel over the top of the cake batter.
Bake 30 minutes in the preheated oven or until golden brown and a cake tester inserted into the cake comes out clean.
Let cool on a wire rack for 30 minutes, then remove from the pan and cut into squares.
Dust with powdered sugar just before serving.