In a medium pot, add buckwheat, water, and a pinch of salt. Cover and bring to a boil. Reduce heat to low and cook for 15 minutes. Do not open the lid. Remove from heat, let stand for 3 minutes, and fluff with a fork.
Meanwhile, preheat skillet or wok over medium heat and swirl with 1 tbsp. of oil to coat. Add garlic and sauté for 10 seconds. Add kale and ¼ tsp. salt; sauté until kale has shrunk in half, stirring occasionally. Transfer to a medium bowl.
Return skillet or wok to high heat and swirl 1 tbsp. of oil. Add peppers and ¼ tsp. salt; sauté until golden brown, stirring occasionally. Transfer to bowl with the kale.
Reduce heat to low and add remaining 2 tbsp. of oil. Add cooked buckwheat and briefly mix until it is coated with oil. Turn off heat.
Add cooked kale and peppers, artichoke hearts, parsley, basil, and remaining ½ tsp. of salt.
Stir gently and serve warm.