In a small bowl, whisk together the Greek yogurt, lemon juice, and lemon zest to make the dipping sauce. Set aside in the refrigerator.
Place 1 cup of the peas in a large mixing bowl and roughly mash them with a potato masher or fork. Leave the remaining 1 cup of peas whole and add them to the bowl.
Add the eggs to the peas and whisk lightly. Stir in the fresh chives, fresh dill, kosher salt, and black pepper.
Sprinkle the all-purpose flour and baking powder over the pea mixture. Stir gently until just combined into a thick batter.
Heat the olive oil in a large skillet over medium-high heat. Once the oil is hot, drop 2-tablespoon portions of the batter into the skillet, flattening them slightly with the back of a spoon.
Fry the fritters for 2 to 3 minutes on each side, or until they are deeply golden brown and crispy.
Transfer the cooked fritters to a paper towel-lined plate to drain excess oil. Serve immediately with the chilled lemon yogurt sauce.