Dice the sweet potato and beets into roughly equal-sized pieces so they cook at about the same rate.
Heat a large cast iron skillet over medium heat. Add the butter and olive oil, then sauté the shallot for a minute or two until it begins to soften.
Add the sweet potato and beets. Season generously with salt and pepper and toss everything together to coat the vegetables in the butter.
Cook over medium to medium-low heat, stirring occasionally, until the vegetables begin to soften and develop browned edges, about 15 to 20 minutes. Add another little knob of butter if the pan starts looking dry.
Once the vegetables are nearly tender, add the sage, rosemary, and cinnamon. Continue cooking for another few minutes until the herbs are fragrant and the vegetables are browned and fork-tender.
Taste and adjust the salt and pepper before serving warm.