Preheat the oven to 200 degrees Celsius (392 degrees Fahrenheit), conventional oven.
Dissolve the yeast in the lukewarm water. Stir in oil, salt, and flour. Knead on a floured surface to form a soft, firm, slightly sticky dough. Let rise for 1 hour at room temperature.
Divide the dough into two parts and roll each out into a base. Poke the bases with a fork and pre-bake them, one at a time, for 5-6 minutes in the preheated oven.
Mix the pesto and tomato paste together and spread over the slightly baked bases. Also distribute chorizo, mozzarella, artichokes, and tomatoes. Sprinkle with salt and oregano.
Bake the pizzas, one at a time, for about 10 minutes until the cheese is melted and the pizzas are golden.
Serve with a little fresh basil.