Cook bacon in a large skillet over medium-high heat until crispy. Transfer to a paper towel to drain.
Leave the bacon grease and place 1 tortilla in the skillet over medium heat for about 30 seconds per side until slightly browned and bubbled. Repeat with the other tortilla and place both on a large baking sheet.
Preheat the oven to hi-broil.
Top the tortillas with the sliced peaches, then burrata. Crumble the bacon into small pieces and sprinkle on top of the tortillas.
Place under the broiler for about 2 minutes until the tortilla edges are browned and crispy and the burrata has melted.
Remove from the oven, top with the pistachios and basil.