In a large thick-bottomed skillet of medium-high heat add a generous splash of olive oil, a generous pinch of salt and the leeks. Stir until the leeks are coated and glossy. Cook, stirring regularly until a lot of the leeks are golden and crispy. I stir every minute or two in the beginning, and more often as they brown using a metal spatula. All in all it takes me roughly 7 - 10 minutes to brown the leeks.
At this point stir in the dill, and then stir in the green beans. Cook for a couple more minutes - just until the the beans brighten up and lose that raw bite. Turn out into a bowl or onto a platter and serve immediately. If you want to prepare these green beans ahead of time - read the head notes.