Slice large tomatoes, and arrange on a large serving platter. Season with part of the sea salt.
Slice cherry tomatoes in half, and toss in a bowl with 1 tsp of sea salt, half of the olive oil, chives, and black pepper. Let stand while you slice the peaches.
Slice peaches thinly. Spoon cherry tomatoes and their juices over the base of large tomatoes. Toss peach slices in same bowl with a drizzle of good balsamic vinegar, remainder of salt, black pepper, olive oil, and parsley. Spoon mixture over the tomatoes on the platter, top with torn basil, and onion flowers (totally optional, they just add a nice savory flavor if you have some overgrown onion plants!)