Prepare the Dough: In a large bowl, combine flour and salt. Add the cubed vegan butter and use your fingers to blend into the flour until the mixture resembles coarse crumbs.
Mix in cold water and apple cider vinegar until a dough forms. Knead gently, then wrap in plastic and refrigerate for at least 30 minutes.
Make the Filling: Boil the diced sweet potato in salted water until tender, about 10 minutes. Drain well.
In a skillet, sauté onion and garlic until translucent. Add the cooked sweet potato, black beans, cumin, and smoked paprika. Cook for a few minutes until the flavors meld. Season with salt and pepper.
Remove from heat and stir in chopped cilantro. Let the mixture cool.
Assemble the Empanadas: Preheat your oven to 400°F (200°C).
Roll out the chilled dough on a floured surface to about 1/8 inch thick. Cut out rounds using a large cookie cutter or a cup.
Place a spoonful of filling on one half of each round. Fold the dough over the filling to form a half-moon shape. Seal the edges by pressing with a fork.
Place the empanadas on a baking sheet lined with parchment paper.
Bake the Empanadas: Bake in the preheated oven for 20-25 minutes, or until golden and crisp.
Prepare the Dipping Sauce: While the empanadas bake, whisk together vegan mayonnaise, chopped cilantro, lime juice, minced garlic, salt, and pepper in a bowl. Adjust seasoning as needed.
Serve: Serve the hot empanadas with the cilantro-lime dipping sauce on the side.