Add the olive oil, vinegar, Greek yogurt and garlic to a small bowl and whisk until combined and emulsified. Set aside until ready to use, you may have to whisk just before serving to recombine the ingredients if they separate.
For the salad:
Bring a large saucepan of water to a boil over medium-high heat. Once the water is boiling carefully add the eggs and cook for 7 minutes. Remove to a bowl of ice water to cool for 10 minutes. Use the backside of a spoon to crack the shell of the eggs and peel under running water. Cut each in half and set aside until ready to use.
In a large salad bowl toss together the romaine leaves, cherry tomato, avocado, radish, basil and chives. Add the dressing as desired and toss to combine. Divide among serving plates and top with the jammy eggs. Serve immediately with sourdough bread.