Tightly wrap beets in foil and roast on a baking sheet until very tender, about 90 minutes. Remove from the oven and allow to cool, about 20 minutes.
When beets are cool enough to handle, peel them, discarding stems and root ends, then cut into ½-inch cubes.
Bring the broth to a simmer. Keep at a low simmer, covered (it's important that the broth is hot when making risotto).
Melt 2 tablespoons of the butter in a large pan or pot over medium heat.
Add the onions and cook, stirring occasionally, until softened but not burnt, about 5 minutes.
Add the barley and cook, stirring constantly, 1 minute.
Add the wine and simmer briskly, stirring constantly, until absorbed, about 1 minute.
Stir in ½ cup broth and simmer briskly, stirring constantly, until broth is absorbed. Continue simmering and adding broth, about ½ cup at a time, stirring constantly and letting each addition be absorbed before adding the next, until barley is just tender and creamy-looking, 25 to 30 minutes.
Stir in the beets and season with salt, and pepper (yes, it will turn hot pink!) and cook, stirring, until heated through.
Remove from the heat and stir in the remaining 2 tablespoons butter, then the cheese. Taste and season with additional salt and pepper as needed, and serve.
Notes
Kosher dairy, Vegetarian
Recipe by Katherine Martinelli at http://www.katherinemartinelli.com/blog/2012/red-beet-and-barley-risotto-2/