About Tomatoes: Go Local if possible - Tomatoes do not become more flavorful and develop adequate flavor unless allowed to ripen on the vine. They will change color and soften, but the sugar, acid, and aroma compounds are locked in once the fruit is taken off the vine. Seek out locally grown tomatoes whenever possible.
Selecting Tomatoes: Select tomatoes that are firm, glossy, smooth, plump, heavy for their size, and free of bruises. Avoid tomatoes that are overly ripe and soft. Fragrance is a better indicator of a good tomato than color. Use your nose and smell the stem end. The stem should retain the garden aroma of the plant itself - if it does not, your tomato will lack flavor and, as far as I am concerned, will be good only for decoration! Remember - If the tomato smells fresh and tomato-y, they will taste that way too!
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, cut side upward (the juices will run out into the pan).
Pour the cream around the tomatoes in the pan, mixing well with the tomato juice. When mixture just starts to bubble, remove tomato halves to individual hot serving bowls.
Pour cream sauce over the tomatoes and serve immediately.
Makes 8 servings (1/2 tomato per serving).