Make the crostini. Cut the baguette into 1/2-inch slices and then brush each slice on both sides with some olive oil. Grill the bread on a grill, grill pan, or electric grill for a couple of minutes on each side. Alternatively, you could bake the bread slices at 360°F (180°C) for about 10-12 minutes in the oven.
To a pan, over medium-high heat, add 1 tbsp of olive oil and the cherry tomatoes. Pan fry for about 8-10 minutes until a bit charred on the outside and a bit soft on the inside (with some of the juices coming out). Alternatively, you could roast them in the oven at 390°F (200°C) for about 10 minutes.
Add the zest and juice of half a lemon (about 2 tbsp of fresh lemon juice) to the charred tomatoes.
Transfer the tomatoes to a serving plate (with all the juices) and then drizzle the fresh pesto over them.
Place the burrata over the tomatoes. Add the remaining lemon zest from the second half of the lemon.
Sprinkle some flaky sea salt (like Maldon) and, optionally, drizzle some extra-virgin olive oil on top. Now for the fun part. Cut open the burrata, and let that delicious burrata mix with the juices of the tomatoes and the pesto. Mop this up with crostinis for a mouthful of utter Mediterrenean magic!