Combine rice, cinnamon sticks, and lemon zest in a medium saucepan.

Toast over medium-low heat, shaking occasionally, until rice develops a nutty aroma (about 5 minutes).

Add water and cook over medium heat, stirring occasionally, until most of the water is absorbed (about 4 minutes).

Add 1 cup of milk and continue cooking until most of the liquid is absorbed (about 6 minutes).

Add the remaining milk and cook until most of the liquid is absorbed (about 7 minutes).

Add sugar and salt, stir well, and cook until sugar is dissolved and the liquid is nearly totally absorbed (about 3 minutes more).

Remove from heat and stir in creme fraiche.

Serve hot, or chill in an ice bath, then refrigerate, covered, for up to 2 days.

Place a sheet of plastic wrap touching the surface of the pudding to prevent a skin from forming before sealing the container.

Leave cinnamon and lemon zest in; they will continue to add flavor. Discard just before serving.

Serve cold, or reheat gently in a saucepan, adding more milk if too thick.