Place the beets in a saucepan and cover with water. Bring to a simmer and cook, covered, until fork-tender, about 15 to 20 minutes. Drain.
Add all the vinaigrette ingredients to a jar with a lid and shake until emulsified. Season to taste.
In a serving bowl, toss the beets with the vinaigrette, arugula, goat cheese, and sunflower seeds.