Add the cauliflower to a food processor and process until broken into small pieces. Transfer to a large bowl.
In a food processor or by hand, grate the potatoes. Drain the liquid from the potatoes using a cheese cloth or paper towels until as much moisture as possible is removed. *This is an important step that will ensure the latkes are crispy, so make sure as much moisture as possible is removed.
Add potatoes to a large bowl. Then add the onion, parsley, flour, breadcrumbs, salt and pepper. Stir to combine all ingredients.
In a large skillet over medium-high heat, add 2 tablespoons oil and swirl to cover pan. Form 2-3 tablespoons of the potato mix into balls and drop into skillet. Cook about 7-8 latkes at a time. Flatten with the back of a large spoon and fry 4 minutes on each side until browned and crispy. For each batch, add 2 tablespoons of olive oil and swirl around pan. If you don’t use enough oil, the latkes will not brown as desired.