Peel the carrots and cut them into thin rounds, or half rounds if the carrots are over 3/4" in diameter. Mince the garlic.
In a large saucepan, heat 2 Tbl. Olive oil. Add the garlic, carrots, and salt. Cook over medium heat, stirring, for 5 minutes.
Add the sugar and water. Bring to a simmer and cook briefly, about 3 minutes. Carrots should still have crunch. Drain the carrots and cool in a bowl for 10 minutes.
In the same saucepan, add 2 tsp olive oil and the onions. Sauté for about 5 minutes over medium heat until they start to brown slightly. Allow them to cool and then add them to the carrots.
Make the dressing by whisking the ingredients together. When the carrots are cool, toss them with the dressing.
At this point you can refrigerate until about 30 minutes before eating. Then toss the carrots with the parsley and nuts.
Serve at room temperature in a pretty bowl as part of a meal.