Cut the broccoli into florets and discard the stalks then finely dice the broccoli so that it is riced. You should have about 2½ cups.
In a medium saucepan pan over medium-low heat, add the olive oil and heat through. Add the shallots and sauté, stirring occasionally until tender, about 3 minutes. Stir in the broccoli and sauté until bright green, about 2 minutes.
Add the rice and sauté, stirring frequently until toasted, about 1 to 2 minutes. Lower the heat to medium-low and add the white wine and stir constantly until the wine is almost completely absorbed.
Add the stock ¼ cup at a time, stirring frequently and waiting for each addition to be almost completely absorbed before adding additional stock.
The mixture should be at a simmer the whole time. Continue this process until the risotto is al dente, about 20 minutes. Stir in the cheddar cheese until completely combined. Serve immediately.
Notes
If you prefer not to use alcohol, simply substitute more broth for the white wine - the risotto remains rich and flavorful.