Cut your tomatoes in half and using a box grater, grate them with a flat hand into a bowl. You should be left with the skin, which can be discarded. Leave it for a couple of hours to let the flavours mingle.
Set up your Big Green Egg for a direct cook with just the stainless steel grid. Set the Egg to 200°C.
Spread a liberal coating of olive oil onto the cut side of your bread.
Place the oiled bread crust up to toast the cut side of the bread. This will take about 2 minutes.
Take the bread off your Egg and rub peeled garlic liberally all over the toasted side of your bread.
Top it with a very generous portion of the grated tomato.
Either sprinkle with salt, or add a couple of anchovy fillets to each portion.
Return your bread to the grill to toast the bottom of the bread.
Serve the bread with a nice glass of chilled white wine, an Txakoli would be perfect in my opinion, but I'd settle for an Albarino.