Carefully remove a thin layer of rind from the lemons using a vegetable peeler. Mince the rind very finely. There will be about 2 tablespoons. Set aside.
Remove all of the white pith from the lemons and section flesh, discarding membranes and seeds. Set aside.
In a small heavy saucepan over low heat, bring the cream, brandy and lemon pulp to a boil. Boil gently for 7 to 8 minutes until slightly reduced.
Cook linguine in lots of boiling salted water until al dente. Place drained linguine in a large, warm bowl and toss with the 2 tablespoons butter. Add sauce and toss to combine. Add Parmesan cheese and toss again.
Serve immediately with the reserved lemon zest and freshly ground black pepper to taste.