Place racks in the upper and lower thirds of your oven and preheat your oven to 400 degrees F. Generously coat two rimmed sheets with cooking spray.
In a medium saucepan, bring the stock to a boil. Add the lentils and cook until tender but not mushy, about 20 to 25 minutes or as specified by the package. Watch the lentils towards the end of their cooking time and add additional chicken stock or water as needed to keep them from drying out.
While the lentils cook, prepare the dressing. In a small bowl or large measuring cup, whisk together the olive oil, red wine vinegar, mustard, and salt (or shake all of the ingredients together in a mason jar with a tight-fitting lid). Pour over the warm lentils and toss to coat. Taste and add additional salt as desired. Set aside.
Place the mushrooms on one prepared baking sheet and the cauliflower on the other. Drizzle each sheet with half of the olive oil and sprinkle each with half the salt and half of the pepper. Toss to coat, then spread in an even layer. Place in the oven and roast until the vegetables are tender and caramelized, 20 to 30 minutes, flipping once or twice throughout. The mushrooms will finish a few minutes ahead of the cauliflower.
Place the arugula in a large serving bowl and top with the lentils and warm roasted vegetables, including any bits of the vegetables that stuck to the pan. Toss to coat. Sprinkle with walnuts and parsley. Enjoy immediately.
TO STORE: Once assembled, this lentil salad is best enjoyed the day it is made. If you'd like to have leftovers, only toss together the portion of the vegetables, lentils, and arugula you plan to eat that day. The roasted vegetables and lentils can be stored separately for up to 3 days.
TO REHEAT: You may enjoy leftover lentil salad cold or you may warm the roasted vegetables and lentils for a few seconds in the microwave until heated through then serve over fresh arugula.