Make the Lemon Vinaigrette. Add fresh lemon juice to a small bowl. Slowly whisk in olive oil so that it emulsifies. Whisk in honey. Add salt and black pepper to taste. Set aside.
Prepare the Salad. Wash and pat swiss chard dry. Remove stems from leaves. (You can discard or reserve stems for another use, such as sauteeing or pickling them.) Stack leaves and roll, chopping into thin ribbons. Add to a large salad bowl with grated parmesan and toss with the lemon vinaigrette. (If you aren’t serving this immediately, see notes below.)
Toast the breadcrumbs. Preheat a frying pan over medium heat. To a small bowl, add breadcrumbs, oil, and garlic, mixing to combine with your hands or a spoon. Once hot, add the breadcrumbs to the pan and brown, moving the breadcrumbs around with a spatula for even browning (and to avoid burning). Remove from heat once the breadcrumbs turn golden brown and toss in the salad bowl with the rest of the salad.
Serve immediately (or see notes below), garnishing with more freshly grated parmesan if desired.