I follow a plant based diet with limited bread, white potatoes, starchy vegetables. We eat tons of fresh veggies with a simple hummus for snacks (chickpeas, tahini, lemon juice). Fruit smoothies with almond milk, and for a treat cocoa. We also eat some nuts (walnuts, almonds,etc.) every day. Tons of fruit, and vegetables galore. Also beans/legumes every day (protein, fiber). If we stick with this we feel great and even lose weight.
I've found recipes for gluten free brownies (no flour, just beans! and no added sugar, just fruit to sweeten). The internet abounds with recipes! Try fatfreevegan.com - some recipes there without too many carbs.
I know that veggie & fruit have carbs, but they are also packed with fibre, vitamins, minerals, antioxidants, and other healthy things. And your body does need some carb to survive - especially your brain!