Line a baking sheet with parchment paper and set it aside.
In a medium-sized pan, combine granulated sugar, brown sugar, baking soda, salt, half-and-half, and butter. Stir over medium heat until the sugars dissolve and the mixture begins to boil.
Continue cooking and stirring until the mixture reaches 235-240°F (use a candy thermometer). Remove the pan from the heat and let the mixture cool for 5 minutes.
Stir in the vanilla extract and pecan halves. Stir vigorously for about 2 minutes until the mixture thickens slightly.
Quickly drop heaping tablespoons of the mixture onto the prepared baking sheet. If the mixture starts to thicken too much, stir in a teaspoon of hot water to loosen it.
Allow the pralines to cool completely at room temperature before serving.