Step 1: In a large, heavy-bottomed pot or Dutch oven, combine the granulated sugar, brown sugar, buttermilk, butter, baking soda, and salt. Stir gently over medium heat until the sugars are completely dissolved and the butter is melted.
Step 2: Increase the heat to medium-high and bring the mixture to a rolling boil without stirring. Insert a candy thermometer, making sure it doesn't touch the bottom of the pot. Continue to cook, without stirring, until the mixture reaches the 'soft ball' stage, which is 240°F (115°C). This typically takes 10-15 minutes.
Step 3: Carefully remove the pot from the heat. Stir in the vanilla extract and the toasted pecan halves. Begin to stir the mixture vigorously with a wooden spoon or heatproof spatula. Continue stirring until the mixture starts to thicken, loses some of its glossy sheen, and becomes slightly opaque (this can take 3-5 minutes). It should be thick enough to hold its shape when dropped.
Step 4: Working quickly, drop spoonfuls of the praline mixture onto parchment paper or a silicone baking mat, forming individual pralines. If the mixture starts to harden in the pot, you can gently warm it over very low heat for a few seconds to make it scoopable again, but be careful not to overcook.
Step 5: Allow the pralines to cool completely and set undisturbed for at least 30 minutes to 1 hour, or until firm. Once firm, they can be carefully removed from the parchment paper and stored.