Preheat oven to 400°F.
While oven is heating, place the cut beets on a baking sheet and toss with olive oil, thyme leaves, salt, and pepper. Roast for 35 to 40 minutes, turning once or twice with a spatula, until the beets are tender. Remove from oven and allow to cool.
While beets are roasting, slice goat cheese loginto coins about ¼ to ½ inch thick. Place on flat plate, cutting board or cookie sheet and place in freezer if you have the space, refrigerator if you don’t.
Assemble the vinaigrette by mixing the honey with the balsamic vinegar until it’s smooth. Stir in the seasoning and then drizzle in the olive oil while whisking. You may need to adjust amount of olive oil amount depending on taste.
When the beets have cooled, toss the arugula with the vinaigrette. Divide arugula between four salad plates. Top with beets. Sprinkle on the pistachio meats, about 1 tablespoon per plate.
Heat a frying pan over medium-high heat. Coat bottom lightly with olive oil to avoid sticking.
Whisk the egg white into a small bowl or saucer, reserving yolk for another use. Spoon breadcrumbs onto a small plate or saucer.
Remove the goat cheese medallions from the freezer/refrigerator. Dip each individually first into the egg white and then coat both sides with breadcrumbs. Lightly toast both sides of each medallion in the pan until golden. Be gentle when you turn them over, they’re delicate!
Divide the toasted goat cheese medallions among the salads, placing them atop the greens and beets. Serve immediately.