Place the unsalted butter in a medium saucepan over medium heat. Stir occasionally as it melts and begins to foam. Keep a close eye as it turns golden brown and develops a rich, nutty aroma—this usually takes about 5-7 minutes. Remove from heat immediately to prevent burning.
In a large mixing bowl, combine the all-purpose flour, rolled oats, brown sugar, salt, cinnamon, nutmeg, and baking powder. Pour in the warm brown butter and vanilla extract. Stir until the mixture is crumbly but holds together when pressed.
Peel and dice the ripe pears into small, bite-sized pieces. Toss them gently to keep them from browning while you prepare the rest of the bars.
Press about two-thirds of the crumble mixture firmly into the bottom of the greased 9x9 inch baking pan to form the base layer. Spread the diced pears evenly over the crust. Sprinkle the remaining crumble mixture over the top, breaking it up so it covers the pears but still has some texture.
Preheat your oven to 350°F (175°C). Bake the bars for 35-40 minutes, or until the top is golden brown and the pear filling is bubbling around the edges. Remove from the oven and allow to cool completely before cutting into squares.
Once cooled, slice into bars and serve. These bars are fantastic on their own or paired with a dollop of whipped cream or a scoop of vanilla ice cream for an extra special treat.