Preheat oven to 400F. Combine cherry tomatoes, garlic, and olive oil in a 9x9 square baking dish and toss to evenly coat. Season tomatoes with salt and pepper.
Roast tomatoes at 400F 25-30 minutes until tomatoes are softened and bursting. Remove tomatoes from oven and finely chop garlic. Toss minced garlic, basil, and oregano into tomatoes. Set aside.
Keep oven on at 400F and place a pizza stone in oven to heat. (if you don't have a pizza stone, instead line a large baking sheet with parchment paper and set aside on counter)
In a medium nonstick pan over medium-high heat, melt butter. Add spinach and saute 3-4 minutes until spinach is wilted. Remove spinach from heat and toss into cherry tomato mixture.
Top flatbreads with tomato-spinach mixture. If using pizza stone, use a peel to slide flatbreads onto stone in oven. If using baking sheet, transfer flatbreads to baking sheet.
Bake flatbreads at 400F 8 minutes, then remove from oven and top with torn burrata cheese and Parmesan cheese. Return flatbreads to oven for an additional 4-6 minutes until cheese begins to melt slightly.
Remove flatbreads from oven and allow to cool 5 minutes. Top flatbreads with a few drizzles of balsamic glaze and additional herbs then slice into wedges. Serve warm and enjoy!