Add the rice a food processor fit with a metal blade and pulse 5 or 6 times. Add the curry and pulse until no big chunks remain, although it shouldn’t not be completely smooth. Pea-sized chunks are okay.
Transfer to a mixing bowl and add the chickpea flour, a teaspoon or two of curry powder and a big pinch of salt. Mix well, using your hands as the mixture starts to come together.
The mixture should be mushy, not stiff. But if it seems soupy or very loose, add a little extra chickpea flour (by the tablespoon) until it holds together. Taste for salt and curry powder. Transfer mixture to the fridge and chill for at least an hour.
Preheat oven to 350 F. Line a baking sheet with parchment paper and spray with cooking spray.
Form the mixture into 6 patties (about 1/3 cup each) and place each on the baking sheet. Spray the tops with a bit of cooking spray. Place in oven and bake for 20 minutes, then flip and bake for an additional 8 to 10 minutes. Burgers should be golden and firm to the touch.