Cut the tops off of the zucchini and reserve. Use a teaspoon or a melon baller to cut the flesh out of the zucchinis leaving a 1/4 inch thick shell. Season with kosher salt and freshly ground pepper and set aside. 

Chop the zucchini flesh into small pieces. Peel the shallots and garlic and mince.

Heat the olive oil in a medium-sized skillet. Add the garlic and shallots. Cook, stirring until the shallots become transparent.

Add the chopped zucchini to the pan and stir to combine. Cook, for 10-15 minutes until the zucchini softens.

Preheat the oven to 350 degrees F. Line a rimmed baking sheet with parchment paper.  Cut 4 additional pieces of parchment paper, each big enough to wrap a zucchini in. Set aside.

Beat the sour cream and crumbled feta together until smooth. Beat in the lemon juice, chopped basil and season with kosher salt and freshly ground pepper to taste. 

Strain the excess liquid off of the cooked zucchini.

Mix the cooked zucchini mixture together with the feta mixture.

Fill each zucchini with the creamy feta/zucchini mixture and replace the lid on each.

Brush each zucchini with one tablespoon of oil and wrap each in a piece of parchment paper and place on the prepared baking sheet. 

Place the zucchinis in the oven, replace the lids and bake for 30 minutes.

Remove from oven and take off the lids of each zucchini. Place them stem side down on the baking sheet.  Return the zucchinis to the oven and bake for another 15 minutes. 

Remove from oven and transfer to a serving dish. Drizzle the excess oil from the baking sheet over the tops of the cheese. Garnish with fresh basil leaves and serve.