The beets take the longest to cook so start them first. Either boil them in water in a small saucepan for 45 minutes, or roast them in the oven at 350°F for an hour fifteen minutes.
Roasting will give you better flavor, but takes longer and uses a lot more energy (unless you are already cooking something in the oven).
When done, set aside to cool for 10 minutes, peel and chop into 1 x 1/2 inch chunks.
While beets are cooking you may want to toast your almond slivers if you are starting with raw almonds.
Just heat a skillet to medium high heat and put in the almonds. Stir frequently with a spatula. When the almonds begin to brown, remove from pan into a small bowl. Let cool, set aside.
Remove any outer leaves that look a bit ragged from the brussels sprouts. Bring a small saucepan half filled with water to a boil and parboil the brussels sprouts for 2-3 minutes.
They should be almost all the way cooked through. (Test by cutting one in half.) Set aside for 5 minutes to cool, cut off any protruding tough stem on each sprout and cut each sprout in half.
4 In a medium sized skillet heat 1 Tbsp olive oil on medium heat. Add the shallot slices and cook until translucent, a few minutes.
Add another tablespoon of olive oil and raise the heat to medium high. Add the sprouts and beets to the pan, along with the thyme and mix well. Salt and pepper to taste.
Cook for 1 minute more, stirring. Remove from heat and serve. Can serve warm or at room temperature.