In a large bowl, combine the warm milk, yeast and sugar. Whisk to combine and set aside for the yeast to activate and bubbles from at the surface, about 10 minutes.
Once the yeast is activated, add the melted butter, salt, pepper, and flour. Whisk everything to combine. Add the grated parsnips and whisk again to combine. The batter should be smooth and have similar texture as pancake batter.
Cover the bowl and set it in a warm place to proof for 1 hour. As the batter sits, it will double in size.
Preheat the oven to 300°F. Line a baking sheet with parchment paper and set aside.
Heat a large frying pan over medium-high heat. Once hot, add 2 tablespoons of vegetable oil. Use a tablespoon to scoop the batter into the frying pan, aiming to make the blinis about 4 cm in diameter.
Cook the blinis for 1 minute and 30 seconds to 2 minutes on the first side, or until bubbles form on top. Use a spatula to flip them over and cook them for an additional 1 minute and 30 seconds.
Once cooked, place the blinis on the parchment-lined baking sheet and place them in the oven to keep warm. Repeat for the remaining batter, adding 2 tablespoons of oil to the pan for each new batch.
Once all the blinis are cooked, arrange them in a single layer on a serving platter. Top each blini with a small dollop of crème fraiche, 3-4 pomegranate arils, and a sprig of parsley. Serve warm and enjoy!