Do all the prep up to a day in advance.
Marinate scallops: Put the beet, salt, lemon juice and water into a blender or food processor and puree the beet. You may need to scrape the sides of the container down a few times. If the mixture is too thick to blend, add some more water until it forms a thick puree. Dry the surface of the scallops and trim off any white dangly bits (these are tough muscles). Put the scallops in a bowl and cover with the puree. Toss it a few times to make sure the scallops are totally covered in the puree, then cover the bowl and refrigerate overnight. You can marinate them for a shorter period, but they will not be as red.
Prep artichoke: Bring a large pot of well salted water to a boil. Remove the tough outer leaves of the artichokes until you reach a part where the bottoms of the leaves are a yellow color. Trim the stem off and any dark green bits clinging to the bottom of the heart (green=bitter). Then trim the top 2/3ds of the artichoke leaves off. If you have trouble cutting through the leaves, you either need to peel off more outer leaves, or you need to trim down lower. Rub the cut edges with a lemon to keep them from turning brown. Add the trimmed artichokes to the boiling water and cook until you can easily pass a toothpick down the middle of the stem (about 10-15 minutes). Use a slotted spoon to transfer the hearts into a bowl of cold water to stop the cooking. Give them a gentle squeeze to remove excess water, and place them on a paper towel lined plate while you prepare the rest of the dish.
Prep the cipollini's: Add the onions to the water you just boiled the artichokes in. Cook until the onions are tender (about 5 minutes). Transfer to a bowl of cold water to cool, then trim the ends and peel the onions. Add to the artichokes and set aside.
Prep the cherry tomatoes: Toss the tomatoes with olive oil, salt and black pepper, then spread them out on a baking sheet. Put them in the oven and turn it on to 400 degrees F. They're ready when they are collapsing and are lightly browned (about 30 minutes).
When you are ready to cook everything, wipe off all the extra marinade from the scallops, lightly salt and pepper them. Get a large chef's pan or two smaller cast iron skillets very hot. Meanwhile heat up a saute pan and add the butter.
Add a splash of oil to pan(s) you are searing the scallops in and place the scallops about 2" apart. If they are too close together, the pan will cool off too much and they'll end up steaming. If your pan was hot enough they should sizzle right away and you should not see liquid pooling in the pan. Meanwhile, add the prepared artichokes and cipollini onions to the pan with the butter, add salt and pepper and saute while the scallops finish.
When you have a nice seared crust on one side of the scallops, flip them over and sear the other side. The color makes it difficult to tell when they are done based on the opacity of the sides, so I relied on the color of the sear and how firm they were (the more firm they are, the more well done they are).
Arrange the scallops on the plate, top with the artichokes, onions and cherry tomatoes. Garnish with the chives. I also threw on some arugula tossed in olive oil for a little extra color.