Arrange the banana peppers, with their stems cut off, on a grill and grill on all sides. Put them in a pot and cover with a lid to smother them.
Prepare 2 jars with twist-off caps. Peel the garlic cloves and chop them coarsely. Arrange the banana peppers almost up to the tops of the jars. Put pieces of garlic and dill sprigs in between them. Arrange round slices of carrots and strips of green pepper at the very top top.
Pour vinegar up to the neck of each jar and top off with water. Then pour the liquid from the jars into a casserole, add salt and sugar and heat it briefly.
Give it a taste and if you don't like it, add more salt or sugar. Pour this marinade back over the peppers, close with the caps and turn upside down to vacuum seal them. Arrange the jars in a dark and cool area.