Clean the Brussels sprouts, cut into the stems in a cross shape, cut larger specimens in half and cook in boiling salted water for 8-10 minutes until al dente.
Mix the butter with the broth, flour and lemon zest in a saucepan with a whisk and bring to the boil, stirring constantly with the whisk. Season the sauce with nutmeg and savory and cook for about 1 minute while stirring.
Drain and drain Brussels sprouts. Chop chestnuts, not too fine. Add Brussels sprouts and chestnuts to the sauce and bring to the boil. Season to taste with a little sugar and a squeeze of lemon juice with salt and pepper.
Bread dumplings, spaetzle, potato dumplings or noodles are suitable as side dishes.