Heat oil in a large nonstick skillet over medium-high heat. Add fennel and next 6 ingredients (through garlic) to pan; sauté 8 minutes or until vegetables are tender. Add 1 cup water; bring to a boil. Cover, reduce heat, and simmer 8 minutes. Uncover and simmer until liquid evaporates (about 4 minutes). Remove from heat; cool.
Place fennel mixture, walnuts, and juice in a food processor; pulse 10 times or until combined (mixture will not be smooth). Spoon into a medium bowl; sprinkle with parsley. Serve warm or chilled.