Toast the bread: Heat the oven to 400°F (200°C).
Toss torn bread with 2–3 tablespoons olive oil and a pinch of salt. Spread on a sheet pan and bake 10–14 minutes, tossing once, until golden and crisp at the edges but still a little chewy inside.
Make the dressing: In a jar or bowl, whisk together 2 tablespoons balsamic vinegar, 1 tablespoon lemon juice, 1 teaspoon Dijon, 1–2 teaspoons honey, the minced garlic, 1/3 cup olive oil, 1/2 teaspoon salt, and several grinds of pepper until emulsified.
Prep the produce: Slice peaches, halve cherry tomatoes, slice cucumber, and thinly slice the red onion or shallot. Tear basil leaves and chop mint.
Mellow the onion: If your onion is sharp, soak the slices in cold water for 5–10 minutes, then drain and pat dry.
This keeps the salad balanced.
Toss the base: In a large bowl, combine toasted bread, peaches, tomatoes, cucumber, and onion. Drizzle over about two-thirds of the dressing and toss gently to coat. Let it sit for 10 minutes so the bread can absorb some flavor.
Add greens and herbs: Fold in arugula (or baby greens), basil, and mint.
Add more dressing as needed so everything is lightly coated but not soggy.
Finish with cheese and nuts: Add mozzarella, burrata pieces, or feta, and sprinkle with chopped almonds or pistachios if using. Taste and adjust salt, pepper, and acidity. A final drizzle of olive oil or a pinch of flaky salt is a nice touch.
Serve right away: This salad shines when the bread is still a bit crisp and the peaches are juicy.