Squeeze the lemon into the water and then place the squeezed lemon into the water as well. Add the 1 teaspoon of salt and bring to a boil.
Place carrots into the boiling salted lemon water and cook for twelve minutes then drain.
Place a large skillet or sauté pan over medium high heat and add the oil. Once hot, add carrots, Herbes de Provence, fennel, salt and pepper and brown slightly for about five minutes.
Add the vermouth and once evaporated, transfer carrots to a serving dish and enjoy.