Dry-toast the walnuts in a frying pan until fragrant and let them cool. Then break them into large pieces with your hands; this gives a nicer result than chopping.
Slice the cooked beets paper-thin using a sharp knife or a mandoline, and arrange them overlapping on a large plate. Season with a pinch of salt and black pepper.
Whisk the olive oil, balsamic vinegar, and mustard together into an emulsified dressing and spoon it over the beets. Let this marinate for a few minutes while you prepare the rest.
Scatter the arugula loosely over the beets and crumble the goat cheese on top. Sprinkle with the walnuts and some thyme leaves. The earthy sweetness of the beets, the tangy goat cheese, and the bitter arugula balance each other perfectly, while the walnuts and olive oil provide the healthy fats that make this lunch truly satisfying.