The old standby is Caprese salad with bufala or Burrata Mozzarella.
Fresh basil has less flavor than dried when cooked, so you can make a batch of amazing fresh tomato sauce with summer tomatoes and whole handfuls of basil. Don't chop the basil, just throw it in the sauce, cook for hours and then pull the basil back out. you can freeze the sauce too and have delicious fresh sauce all winter long.
Eggplant is also a good thing to cook with basil. You can do it Asian style as in spicy Thai eggplant with basil. Or French style as in Ratatouille. Or bake it Italian style with a little garlic and basil. For the last one, cut small eggplant in half lengthwise. score the flesh diagonally not through the skin. grate or finely chop garlic and basil and squish it into the slits. Then spoon and spread a tablespoon or two of plain tomato sauce and drizzle olive oil on top. put in a 375 degree oven in a lightly oiled pan until the eggplant meat is tender, maybe 30-40 minutes. eat with a spoon. This is one of the easiest and most delicious eggplant recipes I know.
You can also marinate chicken in a paste of basil, lemon zest, juice, olive oil and garlic.
BTW, my niece's Tuscan mother-in-law used to tell her that you should pick the basil before it flowers. Once its flowers mature, it will give the leaves a slight bitter flavor.
oops almost forgot. Basil tastes great in omelets.
Finally, if you are just sick of the stuff, you can hang it upside down in a dry place and let it dry out for use in winter.