Set a rack in the center of the oven and heat the oven to 200°F. Put a sheet pan or oven-safe plate inside so you have a warm place to hold the fritters as they finish.

Trim the Brussels sprouts and pull off any rough outer leaves. Thinly shred the sprouts with a knife until you have a loose pile of fine slices.

Grate the peeled potato on the large holes of a box grater. Put the grated potato in a clean kitchen towel or a few layers of paper towels.

Squeeze the potato over the sink until very little liquid comes out. Put the squeezed potato into a large mixing bowl.

Add the shredded Brussels sprouts and sliced scallions to the large bowl with the potato.

In a small bowl, stir together the Greek yogurt, Dijon mustard, 1 tablespoon of the lemon juice, 1/4 teaspoon of the salt, and a few grinds of the black pepper. Set the mustard yogurt aside.

Put the apple matchsticks in another small bowl. Add 1 tablespoon of the lemon juice and a small pinch of the salt, then toss and set the apple salad aside.

Crack the eggs into the large bowl with the vegetables. Beat them with a fork until the yolks and whites are fully mixed.

Add the flour, the remaining 1 1/4 teaspoons salt, and the remaining pepper to the large bowl. Mix well until the vegetables are evenly coated and the mixture holds together when you squeeze a handful of it.

Let the mixture sit in the bowl for 5 minutes. This gives the flour time to absorb moisture so the fritters hold together better in the skillet.

Pour 3 tablespoons of the oil into a large nonstick skillet or a well-seasoned cast-iron skillet. Heat the skillet over medium heat until the oil looks shiny and moves easily across the pan.

Scoop about 1/4 cup of the fritter mixture into the skillet for each fritter, leaving space between them. Flatten each mound with the back of a spoon so it is about 1/2 inch thick.