Start by making the dough: dissolve the activated charcoal in warm water, and the yeast in warm milk. Pour the milk with yeast into the flour and let it sit for 5 minutes until bubbles form.

Add the charcoal water and start mixing with a fork. When it starts to come together, add the salt. Once the dough forms, continue kneading by hand. Add the oil and knead until fully absorbed. Let the dough rest for 15 minutes.

Fold the dough a few times by hand and shape it into a smooth ball. Let it rise until doubled in size.

Preheat the oven to 430°F (convection setting if possible). While the oven heats, spread the dough out in a greased baking pan, make dimples with your fingers, and add the halved cherry tomatoes. When the oven is hot, bake on the lower rack for about 18 minutes.

Tear the mozzarella by hand and let it drain in the fridge while the dough rises. Add the mozzarella to the focaccia and return to the oven until it just starts to melt, about 2 minutes. Place the focaccia on a wire rack and spoon the pesto on top.