In a large heavy skillet over medium heat, toast the ground hazelnuts, stirring frequently, just until it’s a shade or two darker, about 5 minutes. Transfer to a plate; cool.
Adjust the oven rack to a medium rung, and preheat the oven to 325°. Line a baking sheet with parchment paper. In a standing mixer with a paddle attachment, cream the sugar, butter, and vanilla at medium-high speed until fluffy and white, about 5 minutes. Add the toasted ground hazelnuts, and mix just until blended. Add the all-puropse flour and salt, and stir into the nut mixture just to incorporate.
Using a teaspoon or a small cookie scoop (#100), in firmly packed scoops, drop the dough, a dozen or so at a time, onto the baking sheet, then using your hands, roll them into balls; arrange the balls about 2 inches apart. Bake for 8 minutes, remove from the oven, and using the handle end of a wooden spoon, press a “thumbprint” into the center of each ball. Return the cookies to the oven and bake, rotating once, for about 12 minutes more. Transfer to a cooling rack and cool slightly.
In a medium-size bowl, using enough sugar to dust, gently toss a few cookies in sugar at a time, and, shaking off the excess sugar, place them back on the rack. Fill each thumbprint with currant jelly or your jelly of choice.