Preheat the oven to 200°C fan.
Season the brisket generously all over with salt and pepper. Add the oil to a large heavy flame proof casserole - cast iron is ideal - and set over a high heat. When the oil is really hot, add the beef, searing it on both sides for a few minutes until browned. Remove to a large plate.
Reduce the heat to minimum and add the onions and rosemary, stirring well to release the lovely sticky caramelised bits from the bottom. Cook the onions for 10 minutes, and then stir through the garlic. Lift the beef back into the pot, nestling it on top of the onions, then carefully pour over the beer (the pan will be really hot so it may bubble up, so go slowly at first). Tear off a sheet of baking paper and scrunch it up under running water so its wet and pliable. Spread it over the pan, tucking it in at the edges - this will create a steamy lid to keep the beef moist. Cover with a snug fitting lid and slide into the oven. Cook for 30 minutes, and then reduce the temperature to 120°C fan and leave to cook for a further 3-3 1/2 hours until really tender. Remove from the oven. At this point you can leave the beef to cool a little in the juices, or you can continue straight to the barbecue.
To make the corn cakes, add the polenta, flour and butter to a mixing bowl, stir through the smoked paprika and season generously with salt and pepper. Pour over the boiling water, mixing continuously until you have a stiff dough. Crack in the eggs and beat well to mix to a smooth batter.
When you are ready to cook, lay the smoker pipe filled with damp wood chips (if using) to one side of the barbecue, directly on the gas burners and ignite the burner to high.
Drizzle some olive oil over the cut side of the tomatoes and season with a little salt and pepper and place cut side down above the lit burner. They will take about 10-15 minutes to grill, turning over half way. Transfer to the warming rack.
Set a plancha (or large heavy frying pan) onto the other side of the barbecue and fire up the burners underneath it. Drizzle in a good glug of olive oil and spread it about with a heat proof basting brush. When it is hot, dollop generous tablespoons of the corn cake mixture onto it, spreading each with the back of the spoon so it’s about 1.5 cm high. You may need to cook them in a couple of batches, depending on the size of your cooking surface. After about 7-10 minutes, they should be crisp and golden, turn over and cook on the other side before transferring to the warming rack next to the tomatoes.
Now it’s time to barbecue the beef. Set the casserole dish onto the plancha so the gravy keeps warm. Using two sets of tongs, or a couple of fish slices, gently lift the whole piece of brisket onto the hot grill bars where you were cooking the tomatoes and let it caramelise over a high heat for a few minutes. Gently turn and cook the other side.
Whilst the beef is grilling, pour the cornflour paste into the gravy and stir though until thickened.
To serve, slice the beef into thick tender pieces, arrange on a platter, along with the corn cakes and the tomatoes. Spoon a little gravy over the meat and add the rest to a jug to serve alongside.