Preheat oven to 400° F.
Remove the tail and leafy stalk from the beets, rub with olive oil, and sprinkle with kosher salt, and a couple twists of freshly ground pepper. Wrap in foil, along with a couple rosemary sprigs. Place in an oven-proof pan, and roast until tender. The length of time will be dependent on the size of the beets, but it may take a couple of hours. The beets can be roasted ahead and refrigerated until you're ready to use them.
Slice off the tops and bottoms of the oranges, and using a sharp knife, carefully slice away the skin and pith of the oranges so that only the fruit remains. Slice the oranges horizontally into 1/4" or 1/2" thick little slabs.
Peel the beets and slice.
Whisk all of the vinaigrette ingredients together, except the rosemary oil, until the salt is dissolved. Gradually whisk in the olive oil.
Arrange the orange and tangerine slices on a plate. Sprinkle most of the minced rosemary over the slices. Place the beets around and over the oranges and sprinkle on the oregano leaves, and the remaining rosemary.
Drizzle the dressing over the salad.