In a medium pot, add the wheat berries, 1/2 teaspoon salt, a teaspoon of olive oil and water. Cover the pot and turn the heat to medium. Cook for 30 minutes, or until the water is evaporated and wheatberries are tender. Set aside.
In a medium saucepan, add the cubed bacon and cook until lightly golden brown, about 3-4 minutes. Remove with a slotted spoon and drain on paper towels. If needed add a teaspoon or two of olive oil. Turn the heat to medium and when the oil is hot, add the potatoes. Cook for 8-10 minutes, or until the potatoes are cooked and tender when poked with the tines of a fork. Sprinkle the potatoes with the thyme, a few pinches of salt and toss.
Add the leeks and garlic; cook for an additional 2 to 3 minutes, until the leeks have softened and the garlic is fragrant. Deglaze the pan by adding the worcestershire sauce. (Steam should rise from the hot pan. No biggie! Just mix it all up.) Add the pimenton, cooked wheat berries and bacon. Cook for an additional minute or two until the mixture is warmed. Fold in the purslane and then salt to taste. Turn the heat to low while you cook the eggs.
In a small saucepan, fry up a few eggs. Divide the hash between the plates. Top each plate of hash off with a fried egg.