Preheat a medium-sized nonstick pan over medium heat. Add olive oil, minced garlic, thinly sliced shallots, and 1/2 tsp. salt and stir occasionally, until garlic and shallots become translucent and slightly caramelized, about 5 minutes. Add balsamic vinegar and continue to cook until shallots become jammy and reduce in size, about 3 minutes.
Add cherry tomatoes and cover pan with lid for about 8 minutes; the cherry tomatoes will steam and soften, allowing them to release their juices and become saucy. Once tomatoes start to shrivel, gently press on them with the back of a wooden spoon to release their juices (be careful, they can splatter!), and continue to cook until tomatoes are jammy, about 2 more minutes.
While tomatoes are cooking, whisk together tomato paste and 3/4 cup water in a bowl or measuring cup; pour this liquid over the stewed cherry tomatoes when they’re ready. Add remaining salt, black pepper, and chili flake, if using, and stir until well combined. Cook for another 2 minutes.
Using the back of a wooden spoon, create five, evenly spaced indents in the tomato sauce. Crack an egg in each indent, then cover pan and cook on medium heat, until egg whites are set, about 6-8 minutes.
Tear the burrata cheese into six equal-sized pieces and top the shakshuka with the pieces. Top with basil leaves, cracked black pepper, olive oil, and balsamic glaze as desired. Serve alongside toasted bread of choice for dipping. Enjoy!
