Place the grated beets, potatoes, and onion in the center of a clean kitchen towel or cheesecloth. Twist and squeeze firmly over the sink to remove as much liquid as possible.

Transfer the squeezed vegetables to a large mixing bowl.

Add the beaten eggs, crumbled feta cheese, flour, salt, and black pepper to the bowl. Mix until everything is well combined and sticky.

In a large skillet, heat about 1/4 inch of vegetable oil over medium-high heat. To test if it's ready, drop a small piece of the mixture in; it should sizzle immediately.

Working in batches, scoop about 2 tablespoons of the mixture into the hot oil. Flatten each scoop slightly with the back of a spatula to form a disc.

Fry for 3-4 minutes on each side until the latkes are dark golden brown and crispy.

Remove the latkes from the pan and place them on a paper towel-lined plate to drain excess oil.

While the latkes cool slightly, mix the sour cream and fresh chopped dill in a small bowl.

Serve the warm latkes immediately with a dollop of the dill cream.