Cut the bacon into very small dice and brown it in a large heavy pot or Dutch oven until golden brown.
Add the chopped onion and simmer the mixture in the uncovered pot.
When the onion starts to shrink and turns blond, add the cabbage, garlic, caraway seeds and ½cup warm water. Cover and cook until the cabbage starts to get soft.
Add 1teaspoon salt and the pepper. At the same time add the pears, the halved lemon, the red wine and vinegar. Cook covered for 15 minutes.
Add the honey. From this moment on, cook over very low heat.
After about 30 minutes look in the pot to see how much liquid remains. If there is too much and the cabbage is “swimming, ” let more than half of the liquid steam away by cooking without a cover on the pot.
When the quantity of the liquid is just right, taste the cabbage. If it is not sweet enough, add brown sugar to achieve the sweet-sour flavor desired. Take out the lemon pieces. Cover again and cook until the cabbage is almost done. By this time the pears will have disappeared completely and the cabbage will have reduced to a third of its original bulk. Adjust salt if necessary.
Take from the heat. Leave the cover slightly ajar to keep the cabbage warm till serving time. Serve as accompaniment to roast pork or game.