In a large bowl, combine the wine, water, and yeast and stir until yeast is dissolved. Add the honey, 1 teaspoon salt, and 1 tablespoon olive oil and mix thoroughly. Add 1 cup of the flour and mix with a wooden spoon to make a loose batter. Add 2 more cups of the flour and stir for 2 to 3 minutes to incorporate as much flour as possible.
Bring the dough together by hand and turn out onto a floured board or marble surface. Knead 6 to 8 minutes, until you have made a firm, smooth dough. Place the dough in a lightly oiled bowl and cover with a towel. Set aside to rise for 45 minutes. Cut the dough into 2 pieces and set aside to rise for another 15 minutes.
Preheat the oven to 375 degrees F.
Take half of the dough and roll out to 1/8-inch thickness. Remove the pepper from the marinade and arrange them atop the dough, along with the anchovies. Sprinkle with the remaining aromatics and oil from the bowl. Season with salt and pepper, and drizzle with the remaining olive oil. Roll out the remaining dough to a similar thickness and top of the filling. Pinch all around the edges to seal. Cut a vent in the top of the pizza for steam to escape.
Bake on a pizza sheet for 30 minutes or until the top and sides are golden. Remove from the oven to a cutting board and let rest 5 minutes before slicing and serving.