Make the Dough. In a large bowl, combine flour and salt. Add cold vegan butter and work it in with your fingers until the mixture resembles coarse crumbs. Add apple cider vinegar, then slowly add cold water, mixing until dough forms. Add more water one tablespoon at a time if too dry. Knead gently until just smooth. Wrap and refrigerate for at least 30 minutes.
Cook the Filling. Heat olive oil in a skillet over medium heat. Sauté onion and garlic until translucent, about 3 to 4 minutes. Add carrot, celery, and red bell pepper. Cook until softened, about 5 to 7 minutes. Stir in tomato paste, smoked paprika, cumin, chili flakes, salt, and pepper. Add cooked lentils and tofu if using. Cook another 3 to 5 minutes, stirring occasionally. Stir in fresh herbs. Taste and adjust seasoning. Let cool completely before assembling.
Roll Out the Dough. Divide chilled dough into 10 equal portions. On a lightly floured surface, roll each into a 5-inch circle.
Fill and Seal. Place 2 to 3 tablespoons of filling in the center of each dough circle. Fold over into a half-moon and press edges together firmly. Crimp with a fork to seal. Place on a parchment-lined baking sheet. Brush with plant milk.
Bake. Preheat oven to 375°F (190°C). Bake for 25 to 30 minutes until golden brown. Cool for 5 minutes before serving.
Make the Chimichurri. Combine all chimichurri ingredients in a bowl or food processor. Stir or pulse until well combined. Taste and adjust seasoning. Serve alongside the empanadas.