Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a large bowl, cream together the softened butter, granulated sugar, and light brown sugar until light and fluffy, about 3 minutes.
Beat in the eggs one at a time, then stir in the vanilla extract until well combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Stir in the rolled oats until evenly distributed.
Using a tablespoon, scoop out dough and roll into balls. Place half of the dough balls on the prepared baking sheets, spacing them about 2 inches apart.
Make an indentation in the center of each dough ball using your thumb or the back of a spoon.
Place about 1/2 teaspoon of jam into each indentation.
Top each jam-filled cookie with another dough ball and gently press the edges to seal the jam inside.
Bake the cookies in the preheated oven for 10 to 12 minutes, or until the edges are golden brown.
Remove from oven and allow the cookies to cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.