In your 9-inch round cake pan, melt 1/4 cup unsalted butter over medium heat. Stir in 1 cup brown sugar until it dissolves and bubbles gently to form a caramel sauce. Remove from heat and arrange the peeled and sliced pears in a circular pattern over the caramel, covering the bottom of the pan. Set aside.
In a medium bowl, sift together 1 1/2 cups all-purpose flour, 1 teaspoon baking powder, 1/2 teaspoon baking soda, and 1/4 teaspoon salt.
In a large mixing bowl, beat 1/2 cup softened unsalted butter with 1 cup granulated sugar until pale and fluffy.
Beat in 3 large eggs, one at a time, ensuring each is fully incorporated. Stir in 1 teaspoon vanilla extract.
Add the dry ingredients to the butter mixture alternately with 1/2 cup buttermilk, beginning and ending with the dry ingredients. Mix gently after each addition.
Pour the cake batter evenly over the pear and caramel layer in the pan. Smooth the surface with a spatula. Bake in a preheated oven at 350°F (175°C) for 40 to 45 minutes or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for about 10 minutes. Carefully invert it onto a serving plate so the caramelized pears are on top. If any pears stick to the pan, gently lift them back into place.
