Trim the rhubarb and slice it into 1-inch pieces, then peel and finely grate the beet. Combine the rhubarb, grated beet, lemon juice, honey, and a pinch of ground ginger in a medium saucepan. I like to grate the beet finely rather than chopping it because it distributes the color more evenly throughout the compote and breaks down faster during cooking, creating a more cohesive texture.
Bring the mixture to a boil over medium-high heat, then immediately reduce the heat to medium-low and simmer for about 10 minutes, stirring occasionally. The rhubarb will begin to break down and the beet pieces will soften, infusing the compote with deep color and earthy sweetness. You'll notice the liquid starting to thicken slightly as the natural pectin in the rhubarb releases.
Remove the pan from heat and assess the texture. Using a fork, mash the cooked fruit to your preferred consistency—leave it chunky for texture, or mash it more thoroughly for a smoother compote. For an ultra-smooth result, I prefer using an immersion blender to achieve a silky, jam-like consistency that's perfect for swirling into yogurt or spreading on toast. If you want more control, you can remove the beet pieces first for a clearer, more refined appearance.
Transfer the compote to a serving bowl or container and let it cool to room temperature. As it cools, the compote will continue to thicken slightly. Once cooled, it's ready to serve, or you can refrigerate it for up to one week for deeper flavor development.