Place a pot over medium high heat and add in sesame oil. Once hot, add in the cilantro stems, shallots, garlic, ginger, and chilies. Saute for 30 seconds to a minute and then add in the 1/2 cup of stock. Allow the stock to sizzle away and reduce slightly.
After half a minute add in the curry paste and stir to blend all the ingredients together. Heating the curry "wakes it up" and increases the flavour.
Next, in goes the coconut milk, soy and fish sauces and lime leaves. Let this whole mixture get to know each other and reach a light boil. Add in the mussels and cover with a lid. Let steam for 5-7 minutes or until all the mussels have opened. Discard any that do not open.
Once done, remove mussels and broth from pot and place in large bowl. Toss with cilantro, basil, and cherry tomatoes. Serve with grilled bread and steamed jasmine rice.