Preheat the grill to its highest setting.
To make the pesto pasta, place the oil, fresh basil, garlic cloves and sesame seeds into food processor. Season, to taste, with salt and freshly ground black pepper and blend to a smooth consistency.
Place the pesto into a large bowl, add the cooked pasta and toss together to coat.
For the mussels, heat the olive oil in a lidded saucepan over a medium heat. Add the garlic and shallots and sauté for two minutes, until softened.
Add the mussels and white wine, stir well and place the lid on. Allow the mussels to steam for 3-4 minutes, then remove the lid and check that all the mussels are cooked and have opened. Discard any that have not opened.
Select 10 large mussels, open them up and discard the empty half of the shell. Place the mussels on a baking tray, crumble over the blue cheese, season with salt and freshly ground black pepper and place under the grill for two minutes, until the cheese has melted.
To serve, place the pasta in the centre of a warm plate and arrange the mussels around in their shells.