Toss the naan or pita bread and smashed garlic with ½ Tbsp olive oil. Spread on one side of a baking sheet, spread the walnuts on the other. Place in oven and bake until golden and toasty, about 10-12 minutes.
Heat 1 Tbsp olive oil in a pan over medium high, then add the shallot and cook until it just starts to crisp up, about 3-4 minutes. Add the tomatoes, salt, pepper, and crushed red pepper and cook until tomatoes soften, another 2-3 minutes. Add the remaining 1 Tbsp olive oil, red wine vinegar, and honey and cook 1 minute more.
Remove pan from heat and add the spinach, tossing until coated and just beginning to wilt. Mix in the toasted naan or pita, and walnuts. Transfer to a plate, top with torn burrata and chives and serve immediately.