Are the beets supposed to fit in a single layer?

I think the recipe is written with just one layer of beets cooking, with minimal overlap. A lot depends on how large your beets are, likely. The recipe says to use up to 6, but the notes mention using four, and for future to consider using only three. I've seen beets as large as softballs, and as small as marbles, with all points in between. I prefer mine be about 2 1/2 - 3 inches across, and at that size I don't think you'd be getting more than 4 or so in a 10 inch pan. If I had or wanted to do more, then yes- I'd saute in batches with additional tablespoons of butter, and scale up the other ingredients. Then I'd finish it off in a covered baking dish in the oven, set to 375F.