Place rack in middle of oven and preheat to 450°F. Place toothpicks in a bowl of cold water to prevent them from burning while the dates cook.
Remove the outer layer of the parsnip with a peeler. Then lay parsnip flat on a surface, preferably a cutting board, and using the peeler, go from the base of the parsnip to the tip to create the ribbons.
Next, whisk gluten free soy sauce, paprika, and 1/4 cup oil together in a medium bowl. Add parsnip ribbons, toss to combine, and let sit 10 minutes.
Meanwhile, stuff blue cheese (between 1/2 - 1 teaspoon) into each date. Place 1 almond in the center of each. Then wrap parsnip ribbons around each date, using 2 ribbons if necessary to cover middle section. Secure parsnip-wrapped date with a toothpick, trying to go around the almond. Arrange dates on a parchment-lined, rimmed baking sheet. Set extra soy sauce mixture aside.
Bake the dates for 5 minutes. Brush dates with remaining soy sauce mixture. Continue to bake until parsnip ribbons are browned and slightly crisped, about 3-4 minutes longer. Total bake time is 8-9 minutes. Remove toothpicks, if desired. Let cool for 5-10 minutes and then serve dates on a platter.