Set a box grater on a cutting board. Put a clean kitchen towel on the counter, place a large mixing bowl nearby, and line a plate with paper towels for the cooked fritters.

In a small bowl, stir the cottage cheese with half of the chopped dill, 1 teaspoon of lemon zest, 1 teaspoon of lemon juice, a small pinch of salt, and a few grinds of black pepper. Set the bowl in the fridge or aside on the counter while you make the fritters.

In another bowl, toss the sliced cucumber with 1 tablespoon of lemon juice, a pinch of salt, and a few grinds of black pepper. Set it aside so the cucumber softens slightly.

Grate the peeled potato onto the clean kitchen towel. Gather the towel around the potato and squeeze firmly over the sink until very little liquid comes out.

Transfer the squeezed potato to the large mixing bowl.

Grate the cooked beets onto the same towel. Squeeze again over the sink to remove extra moisture from the beets.

Transfer the squeezed beets to the bowl with the potato.

Add the scallion whites and about half of the scallion greens to the bowl. Save the rest of the greens for serving.

Add the beaten egg, the flour, 1 teaspoon kosher salt, and 1/2 teaspoon black pepper to the bowl. Stir until the mixture is evenly combined and holds together when you press a spoonful against the side of the bowl.

Set a large nonstick skillet over medium heat. Add 2 tablespoons of the olive oil and let it heat for about 1 minute.

Scoop 4 mounds of the beet mixture into the skillet, using about a scant 1/4 cup for each fritter. Flatten each mound gently with the back of the spoon until it is about 1/2 inch thick.

Cook the fritters on the first side for 4 to 5 minutes. They are ready to turn when the edges look set and the bottoms are deep golden brown.