1. Cut all vegetables into a 1cm dice, ensuring there is no grit remaining on the leeks. Lightly oil and season the sliced steaks and caramelise thoroughly in a heavy-based and oven-proof sauce pan (approx. 10 minutes). Once well coloured remove the steaks from the pan.
2. Add the carrot, celery, onion and leek to the same pan and gently sweat over a low heat without adding colour. Add the thyme, bay leaf, 1 litre water and half the stock cube, return the beef to the pan and bring to a gentle simmer. Cover the pan with a sheet of parchment, and wrap tightly in foil. Place into a 150°C oven for around 2 hours until the beef is tender.
3. Once tender remove beef from the oven and uncover. Add the remaining prepared vegetables and place on a low heat for 5 minutes. Strip and finely chop the tarragon and parsley.
4. Meanwhile bring 400ml of water, and the other half of the stock cube to the boil. Slowly sprinkle in the polenta, whisking thoroughly. Continue to cook until smooth ensuring to continue stirring to prevent catching. Approximately 10 minutes.
5. Add the herbs into the beef. Place a portion of the polenta into a shallow bowl with a well in the centre. Top with a good ladle of the minestrone.
6. Finish with a spoonful of pesto and some grated parmesan.