Place 3 cups plus 3 tablespoons of flour in a large bowl and make a well in the center. Add yeast, 3 to 4 tablespoons of lukewarm water, and sugar into the well and stir in a small amount of flour from the sides. Set aside until mixture is frothy, about 10 minutes.

Pour in remaining water and olive oil. Mix with a wooden spoon until everything is well combined. Add 1 teaspoon salt and knead vigorously with hands until dough holds together as a ball.

Loosely cover dough with a clean dish towel and let rise in a warm, dry place until doubled in volume, about 30 minutes.

Prepare the topping while dough rises. Stir 3/4 cup plus 2 tablespoons of heavy cream and sour cream in a bowl until smooth. Season with salt, pepper, and parsley.

Preheat oven to 425 degrees F (220 degrees C).

Divide dough into 4 equal pieces. Roll out 2 pieces as thinly as possible into long rectangles. Fold the sides of the dough pieces to form a 1/4-inch edge all around. Spread cream topping evenly across the dough and top each dough piece with 1/4 of the bacon and the onion rings. Transfer the 2 flammkuchen with parchment paper onto a baking sheet.