Tip: Use your best olive oil to indulge both your veggies and your palate.
Stir together rhubarb, 2 cups water, wine, honey and vinegar in a saucepan. Bring to a boil over high heat. Reduce heat to medium and simmer until rhubarb has broken down, about 10 minutes. Pour mixture through a wire-mesh strainer into a bowl, pressing solids to extract liquid. Discard solids. Wipe saucepan clean. Place strained liquid in saucepan. Cook over medium-high heat, stirring occasionally, until reduced to 1/3 cup, about 5 minutes. Transfer to a bowl; stir in shallot, 2 teaspoons of the thyme and 1/2 teaspoon each salt and pepper. Refrigerate for 10 minutes.
Place a steamer basket in a large stockpot with a tight-fitting lid. Add water to just below steamer basket and place stockpot over high heat. Place beets in steamer basket. Cover and cook until beets are tender, 15 to 20 minutes. Transfer to a plate; refrigerate for 10 minutes.
Whisk oil into rhubarb mixture. Add beets; toss to coat. Transfer to a serving bowl. Top with goat cheese, pistachios and remaining 1 teaspoon thyme.