Combine cauliflower, pumpkin puree, garlic, parsley, basil, pumpkin pie spice, black pepper, and pink salt in a large pot; add enough water to almost cover cauliflower. Cover pot and bring liquid to a boil; reduce heat to medium and cook, stirring occasionally, until cauliflower is tender, 20 to 30 minutes. Mash mixture with a potato masher and continue heating until most of liquid is evaporated, about 5 minutes more.
Stir rice flour into mixture, adding more if needed to thicken mixture.
Heat avocado oil in a skillet over medium to medium-high heat. Form cauliflower mixture into patties and carefully place in hot avocado oil; fry until browned, 4 to 5 minutes per side.