Add the vinegar, sugar, 1 teaspoon salt, and 20 millilitres of water to a small saucepan and bring to a boil. Whisk to combine, remove from the heat, and then add the shallots directly to the pan. Set aside to cool.
Preheat the oven to 220C fan.
Add the olive oil, honey, smoked paprika, ½ teaspoon salt, and a few twists of black pepper to a small bowl and whisk together until well incorporated. Pour into a medium parchment-lined tray oven tray and gently combine with the tomatoes, garlic, and thyme.
Place in the oven for 8 minutes, or until just starting to fall apart. Turn the oven off and let the tomatoes sit in the warm oven for 10 minutes.
Discard the garlic cloves and thyme from the tomatoes and transfer them to a wide bowl, with the roasting juices spooned over. Place the burrata in the centre of the bowl, sprinkle with ¼ teaspoon flaked salt and a few grinds of black pepper. Remove the pickled shallot rings from the liquid and place these on top.
Finish with the oregano leaves and serve.
