To make the croutons: Preheat oven to 400°F. Break rye bread into bite-size pieces and toss with olive oil, salt, and pepper on a baking sheet. Spread into one layer. Bake 10–15 minutes, until golden and slightly crunchy. Let cool.
To make the dressing: Combine mustard, vinegar, honey, olive oil, salt, and pepper in a medium bowl and whisk until smooth. Add the red onion to the dressing, letting it soak while the croutons bake.
To make the salad: Gently combine radishes, radicchio, and fennel slices in a large bowl, along with the croutons, dressing, and onions. Shave Parmigiano Reggiano over top and garnish with the fennel tops and mint leaves.