As a vegan, you’re no stranger to earing vegetables for the majority of your meals. You can also consume many vegetables on a diabetic diet as well. There are many low-glycemic vegetables to choose from that are tasty and follow your diet. These include broccoli, mushroom, tomatoes, avocado, spinach, asparagus, and bell peppers. Avoid the starchy vegetables that tend to have a higher glycemic index, including potatoes, beets, and parsnips.