Bring the broth and water to a simmer in a medium pot. Cook the asparagus in the broth until just done, about 4 minutes.
Remove with a slotted spoon. Put in a colander, rinse with cold water and drain. Keep the broth at a simmer.
In a large pot, melt 1 tablespoon of the butter with the oil. Add the onion and cook, stirring occasionally, until translucent, about 5 minutes.
Add the rice and stir until it begins to turn opaque, about 2 minutes.
Add the wine and salt. Cook, stirring, until the wine is absorbed.
Add about ½ cup of the simmering broth; cook, stirring frequently until absorbed. The rice and broth should bubble gently; adjust the heat as needed.
Continue cooking, adding broth ½ cup at a time and letting the rice absorb it before adding more.
Cook the rice in this way until tender, 25-30 minutes in all. The broth that isn’t absorbed should be thickened by the starch from the rice. You may not need all of the liquid, or you may need more broth or water.