Preheat your oven to 500 degrees F.
Line a baking sheet with foil.
Oil 3 bell peppers liberally and bake on the lowest rack for about 30 minutes, turning 3 times during baking. Make sure to turn on your oven fan as this will generate a decent amount of smoke.
Meanwhile drizzle the french bread pieces with olive oil, to taste, and a little salt and pepper. Toss to coat evenly with oil.
Bake in the oven on the middle rack for about 4-5 minutes (do this while the peppers are roasting) until the bread is slightly browned and dried on the outside, but not completely crisp. Remove bread and set aside.
When the peppers are done, remove immediately to a plastic bag and let set for about 30-45 minutes or until cool enough to handle. Feel free to toss them in the fridge to speed up the process.
Then, slice the peppers open and remove the stems, seeds, and skin.
Roughly chop the peppers into large pieces and add to a large mixing bowl.
To the peppers, add the diced tomatoes, mozzarella, herbs, and greens. Toss to combine and set aside to mingle the flavors briefly.
Next, make the dressing by combining the vinegar, olive oil, mustard, and honey in a mason jar. Shake until emulsified. Spoon a tablespoon or two over the vegetable mixture and toss.
Next add the bread and evenly drizzle the rest of the dressing over the bread.
Toss to combine and season further as needed with salt and pepper.
If making ahead, mix everything together except the greens, bread, and dressing. Mix in the salad greens, bread, and balsamic vinaigrette just prior to serving.