Set a large nonstick skillet on the stove and place a paper-towel-lined plate nearby for the cooked fritters.

Put the sour cream into a small bowl. Add half of the dill, 1 teaspoon of the lemon zest, 1 tablespoon of the lemon juice, 1/4 teaspoon of the salt, and a few grinds of the black pepper.

Stir the sour cream mixture until smooth, then set it aside.

Put the sliced cucumber into a medium bowl. Add the remaining lemon juice, 1 tablespoon of the olive oil, 1/4 teaspoon of the salt, and a few grinds of the black pepper.

Toss the cucumber salad well and set the bowl aside so the cucumber starts to soften slightly.

Finely chop the broccoli until the pieces are about the size of peas. Put the chopped broccoli into a large bowl.

Add the cooked rice, shredded cheddar, sliced scallions, and the remaining dill to the large bowl with the broccoli.

Crack the eggs into a small bowl and beat them with a fork until the yolks and whites are fully mixed.

Pour the beaten eggs into the large bowl. Add the flour, baking powder, the remaining 1 teaspoon salt, and the remaining black pepper.

Stir the mixture until it is evenly combined and holds together when you press a spoonful against the side of the bowl. Let it sit for 5 minutes if it looks loose.

Add 2 tablespoons of the olive oil to the nonstick skillet and heat it over medium heat until the oil looks shiny and moves easily across the pan.

Scoop 1/4-cup portions of the broccoli mixture into the skillet, leaving space between them. Flatten each portion gently with a spatula so it forms a small patty about 1/2 inch thick.