Preheat your grill to the highest setting.
Heat a skillet over medium-low heat and add the diced pancetta. Cook, stirring often, until the pancetta is crisp and the fat has rendered. Remove the pancetta with a slotted spoon and place it on a paper towel to drain any excess grease.
In a bowl, stir together the butter, fresh basil, garlic and salt until combined. Slice the baguette into rounds and spread the butter on one side (or both!! If you wish!). Place the slices on a baking sheet to easily take them out to the grill.
Prepare the peaches for the grill! Slice them in half, remove the pits, spray them with olive oil and sprinkle on salt and pepper. Place them on a baking sheet too!
Take everything out to the grill. Put the peaches on first, cut-side down, because they will need a few minutes – about 4 to 5 minutes. You can grill the uncut side for 1 to 2 minutes if you wish.
While the peaches are on the grill, place the bread slices on the grill. They will only need 1 to 2 minutes on the grill, so you can start flipping them as soon as every slice gets on the grill!
Transfer the grilled bread and peaches back to the baking sheet.
Slice the peaches once they are cool enough to touch. To assemble the crostini, pull apart the burrata and place it on each slice of toast. Top with a grilled peach slice (or 2, there are no rules here!). Sprinkle on the pancetta. Garnish with fresh basil.