In a medium bowl, whisk together the flour, salt and baking powder. Set aside.
In a slightly larger bowl, blend together the softened butter and cream cheese until creamy. Slowly mix in the flour mixture until the whole of it is added and combined well into a dough.
Divide dough in half and wrap in plastic; chill in the refrigerator for 2-6 hours.
To make the filling, combine the cherries, sugar, and lemon juice in a medium saucepan over medium heat. Bring the juicy mixture to a light boil and cook until the sugar is completely dissolved, stirring constantly. Add the dissolved cornstarch and stir it in well, keeping the heat on until the mixture begins to thicken. Remove from heat and cool mixture.
Beat goat cheese until it is a smooth consistency.
Butter and flour two cookie sheets and set aside.
Take one half of the dough out of the refrigerator and roll it into a 10-inch circle with a rolling pin and some dusting flour.
Cut the dough into four 5-inch squares. Spoon 1 tablespoon cherries and 1 teaspoon goat cheese onto the middle of each square. Fold the dough over the filling to create a turnover, sealing the edges with a fork. Transfer the turnovers to a floured cookie sheet.
Bake 15-20 minutes, or until the edges begin to brown. Repeat the turnover-making process with the remaining half of the dough while the first batch is baking.
After removing turnovers from oven, sprinkle with coarse sugar or powdered sugar, if desired.