Preheat the oven to 350°F.
Line a baking sheet with parchment paper or a silicone baking mat.
In a large mixing bowl, combine the softened butter and 1 cup granulated sugar.
Cream the butter and sugar together for approximately 4 minutes, or until the mixture is light and fluffy.
Add the egg and vanilla extract.
Mix for approximately 1 minute, or until fully combined.
Add the all-purpose flour, baking soda, and salt to the bowl.
Mix just until the dough comes together. Do not overmix.
Cover the dough and refrigerate for 10 to 15 minutes, or until slightly firm.
In a shallow bowl, combine the remaining 1/2 cup granulated sugar and ground cinnamon.
Roll the chilled dough into 16 to 24 balls, depending on the desired cookie size.
Place each dough ball into the cinnamon sugar mixture.
Roll each dough ball until fully coated on all sides.
Arrange the coated dough balls on the prepared baking sheet, leaving space between each cookie.
Bake for 9 to 11 minutes, or until the edges are lightly golden and the centers remain soft.
If desired, sprinkle the warm cookies with any remaining cinnamon sugar immediately after removing them from the oven.
Allow the cookies to cool on the baking sheet for a few minutes.
Transfer the cookies to a wire rack and allow them to cool completely before filling.
To prepare the filling, melt 1 tbsp butter in a small saucepan over low heat.
Remove the saucepan from the heat.
Immediately stir in the dulce de leche until the mixture is smooth and spreadable.
Turn half of the cooled cookies over so the flat bottoms face upward.
Spread a layer of dulce de leche filling onto the bottom of each turned cookie.
Top each filled cookie with another cookie to form a sandwich.
Press gently until the filling reaches the edges.
Serve immediately, or store in an airtight container.