Place eggs in a large pot and cover with cold water just about an inch over the eggs.
Bring the pot to a rolling boil, cover the pan and remove from heat.
Leave the eggs covered and off the heat for 13 minutes.
Using a slotted spoon, drop the eggs into a large bowl of ice water. Let them cool for a few minutes.
Meanwhile, add pine nuts, basil, Parmigiano-Reggiano, salt and pepper to a food processor bowl.
Begin to pulse and stream in olive oil. Continue pulsing until everything is combined.
Scoop pesto into a large mixing bowl and whisk in Greek yogurt and lemon juice.
Remove the eggs from ice water and peel. Coarsely chop and fold them to the Greek yogurt mixture. Then fold in the sun-dried tomatoes.
Cut the garlic clove in half and rub the cut sides on the charred bread.
Serve egg salad in a bowl with garlic crostini on the side.