oven to 350°F. Bring the oxtails to room temperature. Cook them
by heating the olive oil over medium-high heat in a Dutch oven or a
lidded pan large enough to hold everything. When the oil is hot,
add the oxtails and brown them thoroughly on each side* without
moving them around too much, to let them develop color. As the
oxtails brown, bring 6 cups water to a boil in a separate pot.
When the oxtails are almost brown all over, add the celery and
carrots to the pan. Stir and then add the tomato paste to an
uncrowded spot in the pan, stirring it slightly. Lower the heat and
allow the tomato paste to toast a bit, gently, along with the carrots
and celery.
Add enough of the boiling water to the pan to cover the oxtails
by three quarters. Cover the pan and place in the oven for 2½ to 3
hours*, until the oxtails fall apart when pulled with a fork. When
the oxtails are done, allow them to come to room temperature and
then refrigerate them in their liquid to allow the flavor to develop
overnight.
When you’re ready to assemble the cassoulet, remove the oxtail
pan from the refrigerator and warm it up a bit on the stove over
low heat to reliquify the braising liquid. Meanwhile, bring a small
pan of water to a boil. Drop in the beets and the carrots, along
with a pinch of salt, and lower to a simmer. Cook just until the
beets and carrots are cooked through but still somewhat
toothsome, about 10 minutes; strain and set aside.
Place the oxtails on a large plate* and remove all of the meat
with your fingers, discarding the bones. Strain the braising liquid