Melt the butter in a saucepan and brown the shallots.
Add the lobster flesh and cook for 2 to 3 minutes.
Deglaze with cognac and mix well.

Sprinkle the preparation with flour.
Mix well to coat the lobster flesh, then moisten with the cooking broth.
Cook without stopping mixing until thickened.

Add the smoked paprika, tomato paste, and cream, and mix well.
Divide the preparation into 4 ramekins, then sprinkle with parmesan.

Bake under the oven grill until the parmesan is melted.
Serve immediately.