Beans are ideal crops to grow in many different soil types thanks to their ability to add nitrogen to the soil. For clay soils, bush beans like fava beans and green beans are a good choice; they don’t mind the heavier soil texture during their short growing season, and their roots stay pretty shallow, like lettuce plants.
Summer and winter squash varieties can both be grown successfully in clay gardens. This, by the way, includes zucchini, which is a type of summer squash. These plants love consistent moisture, lots of additional nutrients, and plenty of sunlight.
The deep roots of carrots penetrate clay soil quite effectively. I recommend choosing a carrot variety that’s on the shorter and stockier side for your first season until your soil is on the up and up. Know that growing in heavy clay can distort root vegetables a bit.
This nutrient-rich leafy green performs admirably in clay soil with regular watering. If you’re not a huge kale fan, you could instead grow Swiss chard. They’re both productive leafy greens with fairly shallow roots that benefit from the added moisture retention of clay soil.