Wash, peel, and chop your potatoes. The size of the potato doesn't really matter and blitva is served in multiple potato sizes depending on personal preference. If you're using thin-skinned potato varieties, like a nice red potato, you can even leave some or all of the skin on.
Add your potatoes to a large pot of well-salted (as if for pasta) water and bring to a boil.
In the meantime, wash and then remove the fibrous stalk from your Swiss chard leaves.
Chop the stalk and leaf separately. The stalk should be about ½ inch pieces and the leaf normal bite-sized pieces.
Add the stalks to the pot of boiling water. The stalks are tough and take longer to cook. Boil for 10 minutes.
When the potatoes can be easily pierced with a fork, add the green leaves and cook for 1 - 2 minutes more
Pour out the potatoes and chard into a colander and allow to drain very well.
As the potatoes and chard drain, heat the butter and olive oil up up on the stovetop over medium heat. Use either the same pot that you used to boil the vegetables.
Add the garlic to the oil and butter mixture, allow to become fragrent (60 seconds).
Add your blitva into the pot with the hot melted garlic butter and add salt and pepper to taste. Stir with a wooden spoon to combine. Your potatoes will break apart, this is expected. Do not mash, you want a rustic texture.
Allow to come closer to room temperature, check if salt and pepper is to taste, and serve.