Brown the sausage in the olive oil in a large Dutch oven until it's almost crispy on the outside. You need some of the brown drippings in the bottom of the pan to give the cassoulet its rich flavor.
Remove the sausage from the pan and add the onion, carrots, and parsnips. Brown these for a few minutes to soften the vegetables and add flavor. (Oh, O.K., I deviated from her recipe here too. Shauna said to add the chicken stock here, but I sauteed the vegetables first. Sorry!)
Bring all of this to a boil, then reduce the heat, cover the pot, and allow to simmer for about one hour. Your cassoulet should be thickened and the vegetables nice and tender.