How to Make It
Combine warm water, warm pickle juice, sugar, and yeast in a medium bowl or measuring cup. Let stand 10 minutes.
Meanwhile, whisk together flour, dill, salt, and pepper in a medium bowl. Add pickle juice mixture and 2 tablespoons of the oil; stir until combined and dough begins to pull away from sides of bowl. Turn dough out onto a lightly floured surface, and knead until smooth and stretchy.
Drizzle 1 teaspoon of the oil in a medium bowl; add dough, and turn to coat. Cover with plastic wrap coated with cooking spray, and let stand in a warm place until dough has doubled in size, about 35 minutes.
Preheat oven to 425°F. Remove plastic wrap, and punch down dough. Place on a lightly oiled 18- x 13-inch rimmed baking sheet. Press and stretch dough to edges of baking sheet. Cover with plastic wrap lightly coated with cooking spray, and let stand in a warm place 15 minutes.
Remove plastic wrap. Using the end of a wooden spoon, make indentions evenly over dough. Top evenly with cheese and pickles, and drizzle with remaining 2 teaspoons oil. Bake until lightly golden and cooked through, 15 to 20 minutes.