Combine the olive oil, lemon juice, salt and shallots in a small bowl. Stir and set aside.
In your largest skillet over medium high heat, toss the carrots with a splash of olive oil. Let them cook in a single layer - they'll give off a bit of water at first.
Keep cooking, tossing gently every three or four minutes until the carrots are deeply browned. All told, about twelve minutes.
Add the beans and dill to the skillet and cook for another five minutes, or until the beans as well heated through.
If you are using beans that weren't canned you can allow them to brown a bit as well (just cook a bit longer, and stir less frequently) - they can handle this in a way that most canned beans can't. If you need to add a bit more olive oil to the pan - do so.
Place the contents of the skillet in a large mixing bowl, sprinkle with the brown sugar and pour the 3/4 of the lemon-olive oil mixture over the top. Toss gently.
Let sit for ten minutes. Toss gently once again, taste and adjust with more salt or sugar or lemon juice if needed to balance the flavors.
Serve warm or at room temperature and finish by sprinkling with the almonds just before serving.