Heat the olive oil and butter in a large, heavy-bottomed saucepan over medium-high heat. Add the onion and garlic; cook and stir until the onion begins to turn golden brown at the edges, about 2 minutes. Pour in the rice, and stir until the rice is coated in oil and has started to toast, 3 to 4 minutes. Reduce the heat to medium and stir in the white wine and lemon juice.
Cook and stir until the wine has mostly evaporated, then stir in one third of the chicken stock; continue stirring until incorporated. Repeat this process twice more, stirring constantly. Stirring in the stock should take 15 to 20 minutes in all. Stir in the cream and cook 5 minutes before stirring in the broccoli, chives, Parmesan cheese and Asiago cheese. Cook and stir until the risotto is hot; season to taste with salt and pepper before serving.
Asiago is a hard Italian cheese, similar to Parmesan and Pecorino Romano. If you can't find Asiago, Pecorino Romano is a good substitute, or just use more Parmesan.