Preheat oven to 400 degrees. Spread cauliflower florets out on a baking sheet, drizzle with olive oil, season with salt and pepper and roast for about 15 minutes until just starting to turn golden brown around edges. Remove from oven and let cool.
Add the cooled cauliflower to a food processor and pulse a few times until "riced". You don't want the cauliflower to turn mushy, just enough to be finely chopped. Transfer to a large bowl.
Add the rice, cheddar, breadcrumbs, egg, spices, salt and pepper to taste and stir until well combined.
Form the mixture into 4 patties and place back on baking sheet. Return to oven and bake for about 20 minutes, flipping burgers half way through.
Assemble the burgers on a bun by spreading pesto on the top and bottom of the bun and placing pickled cabbage on top of the burger.
For the pickled cabbage
Add the cabbage to a bowl, pour enough vinegar into bowl to just cover the top of the cabbage and let sit while you make the burgers.
For the pesto
Add all the ingredients except the water to a food processor and process until smooth, scraping down sides as needed. Add water to the processor while running to thin out to desired consistency.