Preheat oven to 350F (standard) or 320F (fan/convection).
Pile mushrooms on a baking tray. Drizzle over oil, toss, then spread on the tray.
Spread beans on another tray, sprinkle carrots all over.
Put beans on top shelf and mushrooms on the shelf underneath.
Bake for 15 minutes or until surface of beans is dried out and splitting and they look thoroughly unappetizing, and the carrots around the edge of the tray are a bit golden. Remove tray with beans from oven.
Move mushrooms to top shelf, bake for further 10 minutes until dried out and wrinkly. Remove from oven, cool.
Place cashews in food processor. Blitz until they are breadcrumb size, don't blitz to powder.
Add beans, mushrooms and carrot. Blitz on high for 10 seconds or until chopped to large crumb size.
Add breadcrumbs, egg, parmesan, garlic, paprika, mayonnaise, salt and pepper. Blitz for 15 - 30 seconds until it comes together like meat burger mixture but you can still see bits in it.
Add rice and shallots, blitz for 2 seconds until just dispersed.
Mixture should hold together well to form patties, but not stick to hands. If too wet, add breadcrumbs. If too crumbly, blitz more.
Shape into 4 - 6 patties, between 0.6 - 0.7" thick and 4" wide. Refrigerate for at least 1 hour.
On stove: Cook burgers cold, straight from the fridge. Heat 2 - 3 tbsp olive oil skillet on the stove over medium to medium-high heat. Add 3 - 4 patties and cook until deep golden and crispy, 4 minutes. Carefully flip then cook the other side for 4 minutes until golden, then transfer to paper towel lined plate to drain.
On grill: Cook cold, straight from fridge. Brush BBQ and Veggie patties with oil. Heat BBQ to medium high. Cook 4 minutes each side until a nice dark crust forms.
