Finely chop most of 1 bunch of dill, reserving just a handful of leaves for garnishing each plate later on.
Melt 3 tablespoons butter in a very large skillet. Add the butter to a medium bowl and whisk in 3 large eggs, the chopped dill and ¾ teaspoon salt. Stir in ¼ cup seltzer, followed by ¾ cup matzo meal until a thick batter forms. Cover loosely with plastic wrap and chill at least 15 minutes and up to overnight.
Bring 4 quarts of water to a boil in a large pasta pot. Season with 3 tablespoons salt.
Lightly oil a small baking sheet.
Grab two small spoons and the bowl of chilled dough. Working one at a time, create almond shaped dumplings with the spoons, transferring them to the oiled baking sheet.
Once all of the dumplings are shaped, gently add them to the pot of boiling water, bring it back to simmer, cover the pot with a lid and set a timer for 30 minutes.
Check for doneness by scooping out one dumpling and cutting into it. If it’s not quite there, continue cooking them for 5 minutes longer.
Meanwhile, coarsely crush or chop 1 tablespoon of caraway seeds.
Thinly slice 5 garlic cloves. Cut 4 tablespoons butter into pads.
In the large skillet over medium heat, melt 2 more tablespoons of butter along with the caraway seeds, sliced garlic, and a few big cracks of black pepper until fragrant.
Add a big ladle of the dumpling cooking water to the skillet to stop the cooking. Bring the sauce to a simmer, then start adding the 4 cold tablespoons of butter, one at a time.
Once the dumplings are cooked, use a slotted spoon to add them to the skillet of rye butter. Set the skillet over high heat and cook, shaking the pan vigorously and turning the dumplings gently to coat them in the caraway butter.
Cut one lemon into wedges for serving.
Divide the dumplings among plates or shallow serving bowls. Top each one with a few more sprigs of dill and some flaky sea salt and a lemon wedge alongside.
