I've been on a Greek yogurt sauce kick recently. It's something that I tend to slip into when the summer comes and I'm looking for something that's cooling, easy to make, and darn tasty to boot. That it goes on just about anything—as a dip for raw vegetables or pita, as a sauce for roasted meats, as a dressing for hearty salads, a rub for grilled corn, and yes, as a sauce for burgers—makes it all the more easy to slip into the trap of making a batch each week and applying it willy-nillilly. It's a trap I really don't mind falling into.
At it's most basic, the sauce I make is a riff on my white sauce recipe, originally designed as a clone of the famous New York halal-cart chicken and rice condiment. A basic mix of thick Greek yogurt, a touch of mayonnaise, garlic, and some sort of acid, it's easy to modify to suit your needs. For this particular version, I felt it needed a bit more of a punchy, salty kick to stand up to the burger, so I added crumbled feta and plenty of black pepper. The feta also helps it to stay put on top of the burger a bit better.
You'll find yourself wanting to put this on everything, if you haven't already finished it off with a spoon by the light of the refrigerator door, that is.
For freshness and crunch factor, I went with some sliced onions and a simple relish made with diced cucumbers and tomatoes. The trick is to salt them in advance and let them drain, concentrating their flavor and seasoning them deeply. A splash of lemon juice adds a bit of brightness to the mix.