Preheat the oven to 350°F.

Place the red beets in a small bowl; drizzle with 1 tablespoon of the olive oil and season with 1/4 teaspoon of the salt and 1/8 teaspoon of the pepper. In another small bowl, repeat this process with the yellow beets. Place the red beets on a square of aluminum foil and wrap to form a packet. Do the same for the yellow beets, and then place both packets on a baking sheet. Roast in the oven until tender, 55 to 60 minutes. Remove from the oven and let cool. Once the beets are cool enough to handle, rub them with a paper towel to remove their skins, trim the tops and bottoms to form a flat surface, and then thinly slice the beets on a mandoline, between 1/8 and 1/4 inch thick.

In a small bowl, combine 2 tablespoons of the olive oil with the balsamic vinegar. Drizzle the red beets with 1 tablespoon of the balsamic–olive oil mixture, season with 1/4 teaspoon of the salt and 1/8 teaspoon of the pepper, and set aside. Repeat with the yellow beets. Reserve the remaining 2 tablespoons of the balsamic–olive oil mixture.

In a small bowl, mix the goat cheese with the chopped pistachios and the remaining 1 tablespoon olive oil.

Toss the arugula and peppercress with the reserved 2 tablespoons balsamic–olive oil mixture, and season with the remaining 1/4 teaspoon salt and 1/4 teaspoon pepper.

Assemble the sandwiches by spreading 1 tablespoon of the goat cheese mixture over each of the 8 slices of toast. Divide the red and yellow beets evenly among 4 slices of the bread, and then spoon 1 tablespoon of the Onion Jam over the beets on each one. Place 1/2 cup of the greens on top of the onion jam on each sandwich, and then cover with the remaining 4 slices of toast. Cut each sandwich in half and serve immediately.