Preheat your oven to 375-400 degrees.
Defrost the broccoli, strain any liquids and press with paper towels to remove as much water as you can. Coarsely chop the broccoli and set aside.
In a medium saute pan, add oil and onions. Cook until translucent and tender. Cool completely.
Meanwhile, combine the remaining ingredients for the Broccoli Cakes and add the onions and broccoli, stirring well to combine.
Using a large ice cream scoop, cookie scoop or measuring cup, add measured amount to the palm of your hands. Moistening your hands helps to prevent sticking.
Form into a tight ball and then flatter into patties.
Transfer to a lightly oiled baking sheet (do not use parchment or a Silpat for this recipe).
Roast for about 10-12 minutes or until showing signs of becoming golden. Flip and cook for another 5-10 minutes.
While the patties are roasting, combine all of the ingredients for the dipping sauce.
Serve with a garnish of fresh parsley and wedges of lemon.