Start the soup: Set a medium saucepan on the stove over medium heat.

Add 1 tablespoon of the olive oil and the chopped onion to the saucepan. Cook, stirring now and then, for 4 to 5 minutes, until the onion looks soft and a little glossy.

Add the garlic to the saucepan. Stir for 30 seconds, just until it smells fragrant.

Pour the crushed tomatoes and vegetable broth into the saucepan. Stir in 1/2 teaspoon of the salt and 1/4 teaspoon of the pepper.

Bring the soup to a gentle simmer. Lower the heat to medium-low, cover the saucepan partway, and let it cook for 15 minutes while you make the fritters.

Mix the fritters: Put the shredded parsnips in a clean kitchen towel and squeeze over the sink to remove as much moisture as you can.

Transfer the squeezed parsnips to a large bowl. Reserve 2 tablespoons of the scallions for serving, then add the remaining scallions to the bowl.

Crack the eggs into the bowl. Add the cheddar and stir a few times to break up the eggs.

Add the flour, baking powder, the remaining 1 teaspoon salt, and the remaining 1/4 teaspoon pepper to the bowl. Stir until no dry flour remains and the mixture holds together when you press it with a spoon. If it looks loose, stir in the extra tablespoon of flour.

Cook the fritters: Set a large nonstick skillet over medium heat. Add 2 tablespoons of the olive oil and let it heat for about 30 seconds.

Scoop 4 scant 1/4-cup mounds of the parsnip mixture into the skillet. Flatten each mound with the back of a spoon or measuring cup so each fritter is about 1/2 inch thick.

Cook the fritters for 3 to 4 minutes, until the bottoms are deep golden brown and the edges look set.