Gather the ingredients.
Place the basil and garlic into a food processor and blitz using the pulse setting. With the processor blades still running, slowly add the olive oil in a steady drizzle. Continue until the oil is combined with the basil.
Add the pecorino Romano, Parmesan, and pine nuts, then blitz again for a few seconds with the pulse setting (avoid overmixing by using a continuous button as this will chop up the ingredients too much). Taste and add salt as needed. Pour the dressing into a screw-top jar and set aside.
Heat a griddle pan to hot, but not smoking. If you have the grill lit, cook the fruit on there. Cut the nectarine into two, remove the stone, then place the four halves onto the pan. Leave for five minutes avoiding lifting or moving or you will tear the fruit. Cook until the nectarines have taken on the pretty char-grill lines, then lift off with a heatproof spatula and put to one side to cool.
It is likely your burrata will be in whey or water. If so, lift from the liquid and dry gently with a paper towel or a cloth. Put to one side while you prepare the salad.
Lay the little gem leaves on the base of a serving dish, then place the fresh burrata in the center.
Cut the nectarines into small bite-sized pieces and place these around the plate the finally add the herbs and tomatoes.
Toast the pine nuts for 3 minutes in a hot skillet then sprinkle over the salad.
Shake the jar of pesto sauce, remove the lid, and spoon a little dressing over the cheese, salad, and tomatoes; be careful not to add too much, or you will overpower the taste of the burrata.
Serve with crusty bread and gently open the burrata to allow the creamy center to be visible and for guests to dip in.