Deep fryers and associated accessories providing increased efficiency and convenience in the production of deep-fried foods. Preferred embodiments herein also may be versatile enough to, besides deep frying foods, be able to steam and boil foods. Preferred embodiments may employ multiple cooking cycles and versatile food support means to fully cook foods. These may provide special advantages for larger unitary foods, such as by way of nonlimiting example, a Thanksgiving turkey. Preferred embodiments may provide advantages including, but not limited to: minimizing countertop usage; reduction in the use of frying oil; compact storage; reduced shipping costs; lowering of warehousing costs; reduced manufacturing costs; and being lighter and more easy to handle in the kitchen. Preferred embodiments of accessory items may simplify and facilitate production of deep fried foods, including cutting foods into shapes appropriate to produce French fries and blooming onions. Other accessories may facilitate the transference and maintenance of frying oil including: returning frying oil to original containers for storage and disposal; and filtering frying oil to prolong its useful life. Methods are disclosed which help purify oil for extended life without use of filtration.