Heat the olive oil in a small skillet over medium heat. Cook the thyme leaves for just a few moments in the hot oil, until fragrant. Remove the skillet from heat and set aside to cool.
Zest the lemon and place in a medium mixing bowl. Juice the lemon and add it to the zest, then whisk in the red wine vinegar. When the thyme olive oil has cooled, slowly whisk it into the lemon and vinegar mixture. Whisk until emulsified. Stir in a generous pinch of salt and pepper.
In a large bowl, combine the cauliflower, fennel, and white beans. Fold in the chives, parsley, and feta. Drizzle with the lemon-thyme dressing and toss to coat. Taste, and add more salt and pepper if needed.