In a small bowl, stir together the plant-based milk and lemon juice. Add ground flaxseed and let sit for 3 to 5 minutes.
Place the grated raw potato in a clean kitchen towel or paper towels and squeeze out as much excess moisture as possible.
In a large mixing bowl, combine the mashed potato, grated potato, flour, nutritional yeast, baking powder, and salt.
Pour in the plant-based milk mixture and stir until well combined. Let the mixture sit for 5 minutes to thicken slightly. If the batter is too thick, add 1 to 2 tablespoons more plant-based milk. If it is too loose, add 1 to 2 tablespoons more flour.
Heat a non-stick skillet or frying pan over medium heat and add 1 tablespoon of vegetable oil.
Scoop out a portion (about 1/4 cup) of the potato mixture and shape it into a pancake about 1/2 inch thick. Place it gently onto the hot skillet.
Cook the pancake for 3-4 minutes on each side, or until golden brown and crispy. If needed, add more oil to the skillet before flipping the pancake.
Once cooked, transfer the pancake to a plate lined with paper towels to absorb any excess oil. Repeat the process with the remaining potato mixture, adding more oil to the skillet as needed.
Serve the vegan Irish potato pancakes warm.