Heat the grill over high heat. When hot, add the corn and cook for 7-10 minutes until the kernels are tender and slightly charred all around. Remove the corn from the grill and set it aside to cool. Slice off the kernels.
In a bowl, combine the grilled corn, peaches, red onion, chopped basil, olive oil, lemon juice, kosher salt, and pepper. Mix until the ingredients are evenly distributed then set aside.
Place an oven rack on the 2nd highest level. Heat the broiler. Line a baking sheet with foil and drizzle on some olive oil. Add the sliced baguette to the baking sheet and arrange them in a single layer. Drizzle more olive oil on top of the baguette.
Place them under the broiler and broil for 2-3 minutes on each side until toasted and slightly golden. Remove them from the oven.
To assemble the crostini, dollop a spoonful of the burrata onto the crostini. Top the burrata with a spoon of the peach and corn salad. Drizzle the honey over each crostini and garnish them with basil leaves. Enjoy!