Puree the carrots in the broth. Squeeze out the gelatine and dissolve it in the hot puree. Season well with salt and pepper and refrigerate for 40 minutes. Whip the cream until stiff and add the basil to the puree as soon as the mixture begins to gel.
Line the loaf pan (1.2 L) with cling film, pour in the mixture. Chill for at least 2 hours.
Roast pine nuts without fat and roughly chop. Finely chop 1 bunch of basil, dice apples. Season everything with vinegar, salt, pepper and sugar.
Turn the terrine out onto a platter, remove the foil and cut the terrine into slices. Serve with the apple mixture.