Preheat the oven to 300°F (148°C) and spread the baguette slices across a baking sheet. Spray with olive oil spray or brush lightly with olive oil. Place in the oven to toast for 10 minutes, checking halfway through to monitor progress.
While the baguettes are baking, peel the mandarins and remove as much of the pith and strings as you can. Separate into individual segments.
Add burrata to a shallow low bowl and cut an X in the top. Add ¼ cup olive oil, garlic cloves, red chili pepper flakes, and rosemary to a large skillet and heat over the lowest heat. Heat for ten minutes, stirring occasionally until fragrant. Pour the heated oil and all of the infused ingredients over the burrata.
Wipe the pan clean with a paper towel and heat the remaining 2 tablespoons of olive oil over medium high heat. Once the oil is hot and almost starting to smoke, place the mandarin segments one side down and let them cook until browned or blistered, 1-2 minutes. Flip and cook for 1-2 more minutes. Pour over prepared burrata.
Arrange the toasted bread next to the burrata bowl and serve immediately. Leave a spoon in the bowl to help scoop the burrata.
