Heat the oil in a medium saute pan over medium heat. Add the artichokes, spinach, chopped garlic and 1 teaspoon of the lemon juice and saute until the spinach begins to wilt and the garlic becomes fragrant, 5 to 7 minutes. Remove from the heat and transfer to a food processor. Add the Parmigiano-Reggiano, feta, parsley and the remaining 2 tablespoons lemon juice and pulse until smooth. Add the kosher salt and season to taste with pepper.
In a small bowl, combine the sea salt flakes and lime zest with your fingers. Set aside.
Rub the remaining whole garlic clove onto one side of each slice of bread. Divide the artichoke mixture equally among the slices, place on a platter and serve; or, spoon into a serving bowl and serve with the bread slices on the side. Garnish with the radishes and lime salt.