In a saucepan over medium heat, bring the water with salt and sugar to a boil and stir until both are completely dissolved. Take the saucepan off the heat; add white wine vinegar, stir, and let the mixture cool slightly. Set aside. 

Wash and chop the dill, keeping the leaves in a small bowl. Set aside. Wash the cucumbers and cut into 0.2-inch (0.5-centimeter) thick slices.

Place your dill and cucumbers into a glass jar; add the brine water.

In a medium bowl, whisk together the mayonnaise, mustard, hot honey and lemon juice. Fill your squeeze bottle with the hot honey mustard mixture.

Fire up your Ooni oven. Aim for 750 °F to 850 °F (400 °C to 450 °C) on the baking stone inside. Use the infrared thermometer to quickly and accurately check the temperature of the middle of the stone.

In a medium saucepan, bring enough salted water to cover the hot dogs to a boil. Reduce the heat so that the water is hot, but not boiling, then add the hot dogs; cook for around 10 minutes.

Place a pizza dough ball on a lightly floured work surface and press air lengthwise from the center of the dough into the crust, creating an indentation the length and width of your hot dog.

Transfer the stretched dough to a lightly dusted peel; add 1.5 ounces of the cheddar to the middle of the dough to prevent it from rising during the bake.

Launch the dough into the oven. Cook for 1 minute, turning once halfway to ensure an even bake.

Remove from the oven; add the hot dog. Reduce the flames to a minimum, then launch the bun and hot dog and bake for another 20 to 30 seconds.

Remove from the oven, top with ketchup, mustard, pickles, crispy onions and garnish with chopped dill (optional).

Repeat the steps for the remaining pizza dogs, serve and enjoy!