Finely chop the onions, shallots and garlic. Zest lemon; keep aside 1 tbsp each chopped shallots and onion, and half of the lemon zest for garnish.
Over medium heat, warm butter and oil in a large cooking pot; add onions and shallots and cook until softened/translucent. Add the garlic and stir through; after 1 minute add the white wine, 1/4 tsp each salt and black pepper and bring to the boil to release the alcohol.
Add 5 sprigs of thyme (wrapped in muslin for ease if you have to hand), reduce heat and simmer for a couple of minutes.
Add the cleaned mussels, and cover with a lid for 5 minutes, giving the pot the occasional jiggle for an even cook. In the meantime, clean the mixing bowl.
Using a slotted spoon, leaving as much of the liquid etc. behind as possible, remove the mussels into the mixing bowl and set aside; discard the thyme stalks. No need to cover the mussels with a lid/foil.