Use it in soups and chowders, French toast, custardy puddings/flan, quiche, stratas/bread puddings (both sweet and savoury), mac & cheese, mashed potatoes, creamed veggies or onions, cakes, gratins... the options are limitless. You can basically use it anywhere where you might use milk, but want a richer/creamier texture (or conversely, where you might use cream but want a lighter texture).
Potato, Carrot and Parsnip Soup
Crème Brûlée French Toast
Melissa Clark's Corn Bread and Broccoli Rabe Strata
Rice Pudding With Caramel & Almond Brittle
Wild-Mushroom Bread Pudding
Marcy Goldman's Bread Pudding Muffins
You can make paneer with it. It's super-easy. Here's Raghavan Iyer's recipe.
Heat half and half until it boils.
Stir in 1/8 cup (one ounce) of white vinegar per 2 pints of half and half and take off heat.
Wait 30 seconds or so (until the curd is done coagulating)
Stain off the whey through cheesecloth in a colander.
Tie the cheesecloth to wrap the curd (e.g., with a twist tie) and put something heavy (such as a pot of water) on top of the cheesecloth-wrapped curd for several hours (to squeeze out the liquid).
I specifically use half & half to make pastry cream for donuts, eclairs, etc. I've used it to make cream soup or chowder, puddings, in risotto, in a gratin, in mac & cheese, cream spinach or other veggie, and in a caramel sauce to name a few. By the way, I have frozen it when I was not able to use it before it expired; to bring it back together, buzz it in a blender.