Pour oil in a frying pan and heat over medium-high heat. Saute fennel, onion, shallots, salt, thyme, red pepper, and garlic 8 minutes or until fennel is soft. Pour in water and let boil. Place lid on pan and simmer 8 minutes. Take lid off and simmer 4 minutes or until liquid is absorbed. Take pan off of heat and let cool.
Using a food processor or blender, puree fennel mixture, walnuts, and lemon juice until fully combined. Pour mixture into a serving bowl and garnish with parsley.