Preheat the oven to 350 degrees F (177 degrees C). Line a baking sheet with parchment paper.
Combine the peanut butter, maple syrup, eggs, vanilla, and salt in a large bowl. Mix well with a whisk. The mixture will be runny and lumpy at first, but will thicken as you keep mixing.
Refrigerate the dough for at least 15-20 minutes to firm up.
Using a medium cookie scoop, place balls of cookie dough onto the baking sheet, about 2 inches apart. Flatten using a fork in a cross-cross pattern to about ¼ inch thickness in the center (the edges may be a bit thicker, which is fine).
Bake for 10-12 minutes, until very lightly golden on the edges but a little underbaked.
Let your healthy peanut butter cookies cool completely. They will firm up as they cool.
