Add the oil to a small skillet over medium-low heat. Add walnuts and toss for about 1 minute. Season with a hefty pinch of salt. Transfer to a plate lined with paper towels to drain.
Remove stalks from fennel. Mince fronds from fennel and set aside. Core bulb and cut into 1/8" thick slices. Core pear and cut into 1/8" thick slices. Crumble cheese into 1/2" chunks. Tear basil into pieces. Combine all these items with the vinaigrette. Transfer to a serving platter and top with the walnuts.
Juice lemon. Combine 2 Tablespoons fresh lemon juice with remaining ingredients in a blender and puree until smooth.