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 the onions are 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.