My beefsteak tomatoes are huge, but one side is ripe and the other is still green. What causes this?

Uneven ripening can be due to many different factors, according to the Missouri Botanical Institute:

When fruit does not ripen evenly throughout and the normal red pigment is absent from localized areas, then a condition of blotchy ripening is indicated. This disorder may appear as yellow to gray-green patches on the fruit. When sliced open, brown discoloration may be apparent. Cultural, weather and nutritional problems may contribute to the condition. Associated with this problem are low potassium levels, cloudy periods and inadequate light intensities. Other possible contributing factors are high soil moisture, high humidity, low temperature and soil compaction as well as excessive fertilization. All of these factors may promote a nutrient imbalance, which results in abnormal pigment formation. Beyond climatic conditions, provide balanced fertility and good cultural conditions to maintain plant vigor.

Raising the potassium level in your soil can be done organically by mixing in wood ash.

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