Dice the speck, finely chop the onion, carrot, and celery, mince the garlic, and peel and dice the potato into 2 cm cubes. Set everything aside near the stove.
Melt the butter in a 5-quart / 4.5 L Dutch oven over medium heat. Add the speck and cook for 4 to 5 minutes, until the fat renders and the edges turn golden.
Add the onion, carrot, and celery. Cook for 6 to 7 minutes, stirring often, until the soffritto softens and turns translucent without browning.
Stir in the garlic and cook for 1 minute, until fragrant.
Add the pearl barley and stir to coat it in the fat. Toast for 1 to 2 minutes, until the grains smell nutty.
Pour in the stock and add the bay leaf and marjoram. Bring to a boil, then reduce the heat to a low simmer and partially cover the pot.
Simmer for 20 minutes, skimming any foam off the surface occasionally.
Add the diced potato and continue simmering uncovered for 20 to 25 minutes, stirring now and then, until the barley is tender with a slight chew and the potato is fork-tender.
Remove the bay leaf and season with salt and pepper, tasting first since the speck and stock both add sodium.
Ladle into bowls and top with chopped parsley and a crack of black pepper. Serve hot.