Preheat oven to 425 degrees. Wrap beets in tin foil and place on a baking dish. Pour ½ cup of water into the foil. Roast until a skewer poked through foil easily pierces flesh, 1 to 1 1/2 hours, depending on the size of the beets. Remove from oven, uncover, and let sit until cool enough to handle. Meanwhile, heat a medium cast-iron skillet over high heat until smokin’ hot. Drop half of the broccoli florets into the dry skillet, being careful not to crowd the pan. After about 30 seconds, toss the florets, and continue tossing as they char and cook, about 2 ½ minutes total. The tender florets will char easily. Transfer the first batch to a plate and repeat with the remaining broccoli.
When beets are cool, rub the skins off with your fingers. They should slip off easily. Lightly crush beets with the flat side of a chef’s knife, then tear into bite-size pieces and place in a large bowl.
Wipe the skillet clean and heat oil, spices, and bay leaves over medium; cook, swirling often, until oil is sizzling and fragrant, about 3 minutes. Pour over beets along with the vinegar; toss to combine. Season with sea salt. Add charred broccoli and toss, drizzle with more olive oil and vinegar, if desired; and serve.