1Lightly grease the inside of a 4-quart saucepan. Line a baking sheet with waxed paper.
2Stir the brown sugar, white sugar, baking soda, sour cream, and corn syrup together in the oiled pan; place over low heat. Cook and stir continually until the sugars are dissolved. Wipe any sugar crystals above the liquid line with a pastry brush moistened with cold water. Bring to a boil over medium-high heat. Do not stir once the sugar syrup begins to boil. Heat to 240 degrees F (115 degrees C), or until a small amount of syrup dropped into cold water forms a soft ball that flattens when removed from the water and placed on a flat surface. Remove from heat; stir in the butter, vanilla, and chopped pecans.
3Drop spoonfuls of the mixture 2 inches apart onto the prepared baking sheets. Press a pecan half into the top of each praline. Allow to cool completely. Store in an airtight container in a cool place.