Put your cauliflower into a food processor and pulse until it breaks up into small pieces that resemble rice.
Pop your cauliflower “rice” into a microwave safe dish, cover in plastic wrap and microwave on high for 2 minutes. Squeeze the moisture out of the cooked cauliflower and return to the bowl.
Meanwhile, add 2 tsp of olive oil to a large nonstick skillet over medium low heat. Cook the onion slowly, stirring every once in a while, until golden and caramelized, about 15-20 minutes. Add to the dish with the cauliflower rice. Allow to cool completely.
Stir in the breadcrumbs, parsley, thyme leaves, the beaten egg, and a pinch each of salt and pepper.
Clean out the nonstick skillet and spritz with olive oil from an oil atomizer over medium high heat. Form the cauliflower mixture into patties (about 3-4 tbsp), and pan fry on each side until golden brown.
Serve with Greek yogurt and applesauce on the side.