In a large bowl, combine water, yeast, honey and olive oil. Mix with a spoon, then let sit until foamy, about 10 minutes. Add the flour and salt, stirring with a spoon until the dough comes together but is still sticky. Using your hands, form the dough into a ball and work in the additional 1/2 cup flour, kneading it on a floured surface for a few minutes. Rub the same bowl with olive oil then place the dough inside, turning to coat. Cover with a towel and place in a warm place to rise for about 1 to 1.5 hours.
While the dough rises, heat 2 tablespoons of the butter in a skillet over medium heat. Add in the sliced onions with a big pinch of salt and pepper. Cook, stirring often, for 10 minutes, until the onions soften. Turn the heat down to low and continue to cook, stirring often, until the onions become golden and caramely, about 20 to 25 more minutes. I don’t over-caramelized them, because they will still cook in the oven!
Preheat the oven to 450 degrees F. Sprinkle a bit of flour or cornmeal on a 10x15 inch baking sheet.
Remove the onions from the skillet and place them in a bowl. Add the remaining tablespoon of butter to the skillet over medium heat. Add in the brussels sprouts and the garlic with another pinch of salt and pepper. Cook, stirring often, until the brussels are softened and bright green, about 6 to 8 minutes.
After the dough has risen, punch it down and place it back on the floured surface. Using a rolling pin or your hands, form it loosely into your desired shape. For this recipe, I just rolled out the dough to fit a 10x15 baking sheet. Nothing specific, just rolled to fit!
Brush the dough with a tablespoon of olive oil, cover all over to the edges. Top with a sprinkling of the cheddar cheese. Add on the caramelized onions, then the brussels sprouts. Top with the remaining cheddar and parmesan. Top with the pistachios.
Place the pizza on the sheet in the oven for 15 to 20 minutes. Check on it after 15 minutes - if it’s not deeply golden and melty yet, give it another 5 minutes. Once golden and bubbly, remove it and let cool before slicing.
Top with a few fresh herbs if you’d like and some grated parmesan!