Preheat the oven to 350°F. Line two baking trays with parchment paper or silicone baking mats.
In a small bowl, mix together the flaxseed and 3 tablespoons of warm water. Allow to sit for at least 5 minutes: this “flax egg” will help the cookies hold together.
Meanwhile, use an electric mixer to beat together the vegan butter and sugar until light and fluffy. Add the vanilla and the flax egg, and beat again until well-combined. Add the flour and salt to the bowl, and mix on low speed until incorporated. Staying on low speed, or using a spatula and working by hand, mix in the chopped pecans. The dough will be slightly soft and sticky.
Use two spoons or a small cookie scoop to portion out heaping tablespoon-sized balls of dough. Gently roll each ball between your palms to smooth them, then place on the prepared baking trays, at least an inch apart. Use the palm of your hand to slightly flatten each dough ball, then use your thumb, a soup spoon, or a measuring spoon to make an indentation in the center of each cookie. If the spoon you’re using is sticking, periodically dip it in warm water as you work to help keep the dough from sticking. Fill each indentation with a small amount of preserves: try to keep the preserves level with the top of the indentation, to prevent overflow.
Transfer to the oven and bake for 15 to 20 minutes, until the cookies are lightly browned and the pecans smell toasty. Cool briefly on the baking trays, then transfer to a cooling rack to cool completely.