Start with the fennel. Trim off the fennel stalks and discard, keeping only the bulb. Remove also the hard root end. Using a sharp knife, cut the fennel into 1/2-inch slices. Wash the fennel slices and drain. Slice the baby carrots in half lengthwise, or in long matchsticks if using a regular carrot.
Heat the oil in a non-stick skillet over medium heat. Once hot, add the fennel and carrots and cook for about 8 minutes, or until the vegetables start to brown.
Next, pour in the soy sauce, maple syrup, and water. Cook over medium heat uncovered for another 10-15 minutes, or until no water remains and the vegetables caramelize. Make sure they caramelize as this step adds a lot of flavor. Remove from heat and let cool at least 15 minutes.
Prepare the dressing: in a small bowl, stir together the olive oil, balsamic vinegar, nutritional yeast, salt, rosemary, and ground pepper until well combined.
In a large mixing bowl, combine the arugula, toasted pine nuts, hemp seeds, and radishes together. Add the caramelized fennel and carrots and pour the dressing. Mix to coat the salad with the dressing.