In a food processor, add the shallot and garlic. Process till finely chopped. Then add basil and the rest of the ingredients, pulsing till smooth and fully combined. Set aside.
In a large bowl, add arugula and top with sliced strawberries and peaches. Tear the burrata into small-ish pieces and place on top. Drizzle with basil vinaigrette and a little fresh cracked black pepper.
Notes
Toss the arugula with the basil vinaigrette if you'd like it fully combined and still look pretty!
Basil vinaigrette will keep well in the fridge for up to 1 week.
Spinach or mixed greens can be substituted for arugula.