Brown rice stir fry with coriander omelette

Name: Brown rice stir-fry with coriander omelette
Ingredients: 200g brown basmati rice; 1 tbsp rapeseed oil; thumb-size piece ginger, grated; 3 garlic cloves, finely chopped; 1 bunch spring onions, finely sliced lengthways; 150g pack shiitake mushroom, sliced; 2 carrots, finely sliced into sticks; 1 red pepper, finely sliced; 3 eggs, beaten with a splash of skimmed milk; small handful chopped coriander, plus extra to serve; 2 tsp soy sauce; 1 tsp toasted sesame oil; 2 tbsp chilli jam; 1 tbsp sesame seeds, toasted