In a small saucepan, heat the walnuts, sugar, and a pinch of salt over medium heat until the sugar begins to melt and the walnuts start taking on a golden color.
Remove from heat when the walnuts are caramelized and just beginning to get some dark brown edges.
Place the walnuts on a dish or waxed paper to cool.
Take 3 pitted cherries and roughly chop them.
Place the cherries into a small bowl or jar and crush them with a muddle tool, the back of a spoon, or the straight end of a wooden spoon to release the juices and flavors.
Add the olive oil, vinegar, honey, thyme, salt, and pepper and whisk. Set aside.
Place the arugula leaves in a large salad bowl and sprinkle the Parmesan cheese over the leaves.
Add the pitted cherries and top with the candied walnuts.
Dress with the cherry vinaigrette just before serving and toss to coat the salad.