Preheat the oven to 300°F (150°C). Line 2 rimmed baking sheets with parchment paper.
One at a time, using the coarse holes of a box grater, grate the parsnips, carrots, and potatoes. Transfer to a bowl, add the shallot, and mix well. Add the flour, baking powder, and 1 tsp salt and toss with your hands to mix thoroughly. Add the eggs and stir with a fork until well blended.
In a wide frying pan, heat 3 tbsp oil over medium-high heat. Fry a test nugget of the vegetable mixture until golden brown, taste, and add more salt to the remaining mixture if needed. Then, working in batches to prevent crowding, scoop up about 1 tbsp of the vegetable mixture for each latke, gently drop it into the hot pan, and pat down slightly to flatten. Cook, turning once, until golden brown on both sides, about 5 minutes total. Using a slotted spatula, transfer to a prepared baking sheet and place in the oven to keep warm until ready to serve. Cook the remaining vegetable mixture the same way, adding more oil to the pan as needed to prevent sticking.
Arrange the latkes on a warmed platter with a small bowl of sour cream alongside, if using. Serve right away.