Preheat the oven to 350 degrees Fahrenheit. Line a baking sheet with a silicone baking mat or parchment paper. Set aside.
Place the dates, peanut butter, ground flax, water, vanilla, baking soda, and vinegar in a food processor. Process just until a sticky, fairly smooth batter is created. Do not overprocess.
Scoop out the dough in tablespoons. Roll dough into a ball with your hands. Place rolled dough on prepared baking sheet. Repeat with the remaining batter, spacing each ball about an inch apart.
With a fork slightly press down and flatten dough crosswise. Don't flatten as much as you would a regular cookie.
Once cookies are flattened, with your thumb make a deep indention in the centre of each cookie.
Using 1/4 cup of the jam, spoon it into each indention, filling them.
Place cookies in the oven and bake until the edges of the cookies start to lightly brown, about 13 to 15 minutes. Check after 13 minutes to insure the cookies aren't burnt. They can burn quickly.
Once done remove baking sheet and transfer cookies to a baking rack. They will still be soft but will harden as they cool. Let cookies cool completely before serving.
While the cookies are hardening, place the remaining jam in a small microwavable bowl. Microwave it on high for 30 seconds. Spoon into the indentation of each cookie, filling them.
Store cookies refrigerated or freeze for later.