Grate the mushrooms, ham and gouda. Set them aside.
Mix the cream cheese, ketchup and tomato puree in a small bowl until smooth. This is your pizza spread.
Preheat the oven to 200°C (400°F) and line baking trays with parchment paper.
In a large bowl, mix the flour, baking powder and salt. Add the Greek yogurt and olive oil.
Knead by hand, or use a stand mixer for an easier job. The dough should be soft but not sticky and come together in one compact ball. If it feels dry, add a little more yogurt. Different gluten free flours absorb differently, so you may need to adjust.
Dust your work surface well with flour. Roll out the dough to about 5 mm (1/4 inch) thick. Dust the top with flour too so it does not stick to the rolling pin.
Cut out your shapes with fall cookie cutters. No cutters? Use a small drinking glass, and dip its rim in flour first so it does not stick.
Place the shapes on the lined trays. You will need at least 2 batches, as they will not all fit on one tray.
Spread each bite with the cream cheese mix. Top with mushrooms, ham and gouda, then sprinkle with oregano.
Bake for about 15 minutes. The dough puffs up a little from the baking powder but keeps its shape.
