In a large bowl, beat ½ cup unsalted butter until creamy, about 1 minute. Slowly add 1 cup brown sugar while beating for about 3 minutes, until light and airy.
Add 2 eggs, one at a time, beating well after each addition.
Add 1 ½ teaspoons vanilla extract and mix.
Sift the dry ingredients: 1 ⅔ cups all-purpose flour, 2 teaspoons baking powderand ½ teaspoon salt. You can use a medium bowl or have them measured and sift them directly over the butter mixture, whatever works for you.
Add them in 3 additions to the butter mixture, alternating with 1 cup sour cream in 2 additions. That means you begin and end with the flour mixture. Mix to integrate well at low speed or with a spatula, but don’t overbeat or the cake will be tough.
Pour the cake batter in mounds carefully over the pears (the caramel will have hardened). With the back of a spoon, a spatula or an offset spatula, spread the batter to cover the fruit completely.
Bake for about 45 minutes, or until a cake tester or toothpick inserted comes out clean. Some juices might appear around the rim. That is a good sign!
Remove from the oven and let stand for 3 to 5 minutes on a wire rack. Have ready the serving platter. You must be quick and invert the cake while still very hot to prevent the caramel from hardening.
Run a smooth-bladed knife around the edges to unstuck the batter where needed, and lightly shake the pan sideways to loosen the fruit and caramel. Place the serving plate upside down on top of the cake pan, with a kitchen towel (the pan is very hot) grab both the plate and the pan simultaneously and then carefully invert the cake.
Lift the pan carefully. Some fruit or pecans might still be stuck. It happens. Remove them with a knife or spatula and arrange them on the cake where they were originally.
Let the cake cool on a wire rack.
Serve it warm with whipped cream, or plain at room temperature.
Store it covered in plastic wrap or a cake dome for 1 day, then refrigerate it, well covered to prevent dryness.