Preheat oven to 350°F
Brown 1 stick of butter in a small saucepan on medium heat until the butter turns brown and milk solids separate, stirring frequently. Remove from heat and transfer to a bowl to cool
Line a 9-inch round cake pan with parchment paper and spray with oil or grease generously. Lay the pears down in a spiral
Melt 6 tbsp butter in a small saucepan. Turn heat to high and add maple syrup, ¼ cup granulated sugar, and rosemary sprigs. Bring to a boil and cook for about 3 minutes until frothy and caramelized. Remove rosemary with tongs and discard. Pour caramel mixture over pears evenly
In a medium bowl, mix together flour, baking powder, cinnamon, ginger, and salt
In a separate medium bowl, mix together cooled brown butter, sugar, brown sugar, eggs, vanilla, and milk
Mix wet mixture into flour mixture until evenly combined. Spread batter evenly over pears
Transfer to oven and bake for 45-50 minutes or until the top springs back when lightly touched
Let cool for 10 minutes and loosen edges with a paring knife. Place a plate on top of the cake and invert both at the same time
Serve warm or at room temperature. Optional: dust with powdered sugar
