Place a heavy based pan over a medium heat.
Add the olive oil and 50 g butter and heat until foaming.
Season the rabbit shoulders, place them into the pan and lightly colour them.
You may have to do this in batches.
Remove them from the pan, add the mushrooms and shallots, season with a pinch of salt and seat until the vegetables are softened and just starting to colour.
Place the rabbit shoulders back into the pan, add the bay leaf, cover with the chicken stock, cover with a lid and transfer to an oven preheated to 125 °C and cook for 1 hour.
Remove from the oven and set aside to cool.
Tip the contents into a colander set over a large bowl.
Strain the resulting stock through a fine sieve; reduce to 350 ml and reserve.
Pick the meat off the rabbit shoulders and discard the bones and spent vegetables.
Cook the pasta in salted boiling water until al dente.
Drain it well, add the rabbit stock, remaining butter and tarragon leaves and heat until it is all emulsified into a rich coating sauce - this may take a minute.
Transfer to 8 preheated bowls and finish with a generous grating of parmesan and a few garlic or chive flowers.