Combine the yeast (2 ¼ tsp/7 g), sugar or honey (1 tsp), and 1 tsp of the flour with ½ cup (120 ml) of warm water. Wait about 10 minutes for it to foam.
Pour in the remaining flour (3 ½ cups/450 g), the rest of the water (scant ½ cup/100 ml), half the olive oil (2 tbsp/30 ml), and 1 tsp of salt. Stir into a shaggy dough.
Knead the dough for 8 minutes, either in a kneading machine or by hand on a floured board, until it’s smooth and springs back when you press it.
Shape it into 2 balls, cover them, and leave them somewhere warm for about an hour to double.
Turn the oven on to 450°F (230°C). Blend the cream cheese (scant ½ cup/100 g) with the sour cream (3 tbsp/45 g), and grate the mozzarella (7 oz/200 g) and cheddar (5 oz/150 g).
Brush any dirt off the porcini (10.5 oz/300 g); don’t rinse them. Cut them into slices, slice the onion, and chop the garlic (3 cloves).
Warm the butter (2 tbsp/30 g) with the remaining olive oil (2 tbsp/30 ml) in a wide pan and cook the onion until soft.
Tip in the porcini and garlic, season with the remaining salt (1 tsp) and the pepper (2 tsp), and cook for 3 minutes, stirring often, until the mushrooms brown. If the pan dries out, add a splash of water or white wine.
When the dough is ready, press and stretch each dough ball into a large circle and lay it on a baking sheet lined with parchment.
Spread half the sauce on each base, season with salt and black pepper, then layer on the mozzarella and the cheddar.
Divide the porcini between the pizzas and dust them with the oregano (½ tsp).
Bake for 13 to 15 minutes, until the edges are crisp and browned and the cheese is bubbling. Slice and eat hot. Enjoy :)