In a medium bowl, use a hand mixer on medium speed to beat the softened butter and erythritol until the mixture is pale yellow, light, and fluffy.
Mix in the bourbon, vanilla extract, and chopped pecans until everything is just combined.
Cover the bowl and chill in the refrigerator for 30 minutes, or until the mixture is firm enough to handle.
While the bourbon mixture chills, prepare the chocolate coating.
Place the sugar-free chocolate chips and avocado oil in a small, microwave-safe bowl. Microwave in 30-second intervals, stirring well after each one, until the chocolate is completely melted and smooth.
Prepare a baking sheet by lining it with parchment paper, or set out 12 individual foil candy cups.
Remove the chilled bourbon mixture from the refrigerator.
Using a small cookie scoop or a tablespoon, portion the mixture and roll it between your palms to form 12 uniform 1-inch balls.
Working one at a time, use a fork or spoon to dip each ball into the melted chocolate, turning to coat it completely. Lift the ball out, allowing any excess chocolate to drip back into the bowl.
Place the coated ball in a candy cup or on your prepared baking sheet. Immediately top with a pecan half before the chocolate sets.
Refrigerate the finished bourbon balls for at least 1 hour to allow them to fully set. For the best texture and flavor, let them sit at room temperature for about 10 minutes before serving.
Let the bourbon balls rest at room temperature for 10 minutes before serving. This slightly softens them for the best melt-in-your-mouth texture.
