Cut tomatoes in half widthwise.
In a large frying pan over medium heat, melt butter. Reduce heat to low and place tomato halves, cut side downward, in the melted butter. Cook for 5 minutes, then turn tomatoes over
and sprinkle with coarse salt. Continue cooking for an additional 10 minutes; turn tomatoes again (the juices will run out into the pan). Turn tomatoes cut side upward. Add cream around the tomatoes in the pan, mixing well with the juice. When mixture starts to bubble, remove tomato halves to individual hot serving bowls.
Pour sauce over the tomatoes and serve immediately.
Makes 8 servings (1/2 tomato per serving).