In a frying pan, heat one tablespoon of the vegetable oil over a medium heat. Add the onions and garlic and fry for 2-3 minutes, or until softened.
Add the paella rice, ground turmeric and smoked paprika and stir well to coat the vegetables in the spices.
Add the hot stock and chopped rosemary and bring the mixture to the boil, stirring well. Reduce the heat to a simmer and simmer the mixture, stirring occasionally, for 18-20 minutes, or until the paella rice has absorbed most of the liquid.
Add the cherry tomatoes and peas and continue to simmer for a further 4-5 minutes, or until the rice is just tender.
Remove the pan from the heat and drizzle over the olive oil, then stir until well combined. Stir in the chopped parsley.
Meanwhile, heat a griddle pan over a medium heat. Rub the drained artichokes all over in the remaining three tablespoons of vegetable oil. When the pan is hot, add the oiled artichoke hearts and griddle for 1-2 minutes on each side, or until golden-brown griddle marks appear on both sides (NB: Do not stir the artichoke hearts as you griddle them).
To serve, spoon the paella into the centre of four serving plates. Place some of the griddled artichokes on top of each serving.