To Make the Dough
Combine flour, yeast, and salt in the bowl of a stand mixer fitted with a dough hook attachment. Stir to combine, then add water.
Mix on low speed until dough comes together into a rough ball, then shut off mixer and let rest for 10 minutes.
After 10 minutes, continue mixing at medium-low speed until dough forms a smooth, silky ball, about 10 minutes longer. (It will stick to the bottom of the bowl as it kneads rather than riding around the edges.)
Remove dough hook and form dough into a tight ball, set in the bottom of the mixer bowl, cover tightly with plastic wrap, and set aside in a warm place until dough has roughly doubled in volume, about 90 minutes.
To Form the Dough
Pour 4 tablespoons olive oil in the bottom of a 10-inch cast iron skillet.
Transfer dough to skillet and turn to coat in oil.
Press down on dough and spread it toward the edges (you won’t be able to get it all the way to the edges; relax, this is okay.)
Spread it as much as you can without tearing, then cover tightly in plastic and set aside for 30 minutes to allow dough to relax. Return to dough and stretch it out again. It should be able to reach the edges this time. If not, let it rest a little more and try again. To get the dough to stay in the corners, stretch it up beyond the corners so that it pulls back into place.
Once dough is stretched, cover again and set aside while you make the sauce.
To Make the Sauce
(*Now is the perfect time to preheat your Big Green Egg! Heat to 500°F and set up for direct grilling.)
Heat 2 tablespoons of olive oil in a medium saucepan over medium heat until almost smoking, about a minute.
Add minced garlic, oregano, and red pepper flakes and cook, stirring until fragrant, about 30 seconds.
Add tomatoes, garlic powder, onion powder, and honey.
Bring to a simmer and cook until reduced to about 3 cups, about 30 minutes. Season to taste with salt after the sauce has reduced.
Topping the Pizza
Gently press down any large air bubbles if you see any.
Lay half of pepperoni evenly over face of dough.
Spread the 3/4th of the gouda cheese evenly along the edges of the dough where it meets the skillet. (This is the key step that gives this pizza its special crispy, cheesy charred crust!)
Spread the remaining cheeses evenly over the dough (don’t forget those edges!), then add remaining pepperoni.
Spoon sauce over surface in random dollops (you will need only about half the sauce—save the rest for another pizza ‘cause you’ll def want to make one after you devour the first).
Place the cast iron skillet on the Big Green Egg and close dome. Allow the pizza to cook until edges are near black, bubbly and exposed cheese on top is starting to lightly brown, 13 to 15 minutes. Remove from EGG and place skillet on a trivet or oven-proof towel.
Carefully (the skillet will be very hot!) run a thin metal spatula all the way around the edges of the skillet to loosen the pizza. Lift it out and slide it onto a cutting board. Cut pizza in squares and try to share.