Mix 50 g (2 oz) polenta on a plate with 2 tablespoons of Parmesan. Beat the eggs in a shallow dish. Dip the chicken slices into the egg, then roll in the polenta mix until thinly coated. Put on a plate and set aside.
Put the sun-dried tomatoes into a shallow ovenproof dish, then put the fresh tomatoes on top, add 1 tablespoon oil, the pesto and a little seasoning. Grill for 5 minutes.
Bring the measured water to the boil in a nonstick saucepan, add the remaining polenta, bring back to the boil and stir constantly until thickened and smooth. Mix in the remaining Parmesan and season generously. Set aside.
Heat the remaining oil in a frying pan, add the chicken and fry for 8–10 minutes, turning until golden and cooked through. Reheat the soft polenta, gradually mixing in the cream and a little extra water if needed, until soft.
Spoon the polenta on to plates, top with the tomatoes, then arrange the chicken strips on top. Garnish with basil leaves, if liked.