For the rolls: Combine the milk, yeast and 1 teaspoon sugar in a bowl and swirl together. Let sit until foamy on top, about 5 minutes.
Combine the cinnamon, salt, cardamom and 3 1/2 cups flour in a large bowl or the bowl of a stand mixer fitted with the dough hook. Whisk together the eggs, oil, honey and vanilla in a medium bowl. Stir the yeast mixture and oil mixture into the dry mixture and then knead, either on a work surface or with the dough hook, adding up to 1 cup more flour as needed, until the dough is smooth and slightly sticky, 15 minutes by hand and 7 to 10 minutes by mixer. Place in an oiled bowl, cover with plastic wrap and let rise until doubled in size, 1 1/2 to 2 hours.
For the filling: Spray a 9-by-13-inch baking dish with cooking spray and set aside.
Turn the dough out onto a clean surface and roll it out, dusting with flour as needed to prevent sticking, into an 18-by-12-inch rectangle. Spread it with the apple butter and sprinkle with the cinnamon and almond paste. Roll up tightly starting from a long end (so that it results in an 18-inch-long roll), and pinch the edges to seal. Cut into 12 rolls and place in the prepared baking dish. Cover with plastic wrap and refrigerate overnight. (Or cover loosely with plastic wrap and let rise at room temperature for 1 hour, then go right to preheating the oven.)
When ready to bake, remove the rolls from the refrigerator and loosen the plastic wrap. Let sit at room temperature until puffy, 1 to 2 hours.
Preheat the oven to 350 degrees F.
Beat the egg with a splash of water in a cup. Remove the plastic wrap from the baking dish and brush the rolls with the egg wash. Bake until the rolls are lightly browned and have an internal temperature of 190 degrees F, 35 to 40 minutes.
For the frosting: Meanwhile, blend the blanched almonds in a food processor, scraping the sides occasionally, until creamy and spreadable, 5 to 10 minutes. Add the honey, almond extract, salt and lemon zest and continue to blend (it may clump together at this point, and that's okay) as you drizzle in the milk. Blend until creamy. (This can be made the day before and stored in an airtight container in the fridge.)
When the rolls come out of the oven, spread them with the frosting, sprinkle with the sliced almonds and serve.