Combine the water, cauliflower, and carrots in a medium saucepan and bring to a boil. Cook for 4 minutes, then drain well. Place the cauliflower and carrots on a few layers of paper towels and pat dry. Transfer to a cutting board and finely chop.
Place the chopped veggies in a large bowl; add flour and stir to coat. Fold in the cheese, salt, pepper, green onions, and egg.
Heat the olive oil in a large skillet over medium-high heat, swirling to coat. Put the fritter mixture into the skillet ¼ cup at a time, using a spatula to flatten each fritter into shape. Cook until golden brown, about 4 minutes, then carefully flip over and cook for about 4 minutes more. Transfer to a paper towel-lined plate to absorb excess oil if needed.
Smoky Garlic Aioli
Drain and rinse the cashews. Combine the cashews, garlic, lemon juice, paprika, and ¼ cup of water in a blender and blend until smooth. If needed, add additional water 1 tablespoon at a time. Season with salt and pepper to taste and serve with the fritters.
This recipe makes a little extra aioli. Use it on burgers and sandwiches or as a dip for veggies. It will last in the fridge for a few days.