Morning

Make the pickled beet stems: Put the beet stems in a heatproof nonreactive container (such as a canning jar or glass storage container, or a bowl). In a small saucepan or in a glass measuring cup in a microwave oven, bring the vinegar, honey, salt, and all-spice to a boil and stir to dissolve the salt and honey. Pour the liquid over the beet stems. Let cool for a few minutes, then cover and refrigerate.

Morning or Evening

Make the eggplant quark: Preheat the broiler to high and set a rack about 6 inches (15 cm) from the heat source.

Cut a large eggplant lengthwise into eighths, or small ones in half. Put them cut sides up on a baking sheet, drizzle with the oil, and sprinkle with salt and a few grindings of pepper. Broil until the eggplants are very soft and deeply browned, 15 to 20 minutes. Let cool for a few minutes, then scrape the flesh onto a cutting board and discard the peel and stem. Finely chop the flesh and scrape it into a bowl. Add the quark and stir it in vigorously with a fork. Add the lemon zest and juice, and season with more salt (about ½ teaspoon) and pepper, if needed.

Evening

Spread the bread with the eggplant quark, top with the beet stems (chop them first for easier eating, or leave them whole for dramatic effect), and serve.