Make the dough: Place milk in a heatproof bowl and warm it up on the stove or in your microwave, until it’s warm but not hot to the touch. Gently stir in yeast and allow it to dissolve.
Transfer flour to the bowl of your stand mixer (or use a large bowl for hand-mixing. Pour in the milk with yeast, sugar, melted butter, whisked eggs, salt, lemon zest and rum. Using a dough hook (or a wooden spoon if mixing by hand), mix the ingredients on low speed until the dough starts to take form.
Knead for about 5 minutes, until the dough is starting to form a ball and is pulling away from the bowl. If it’s too sticky and isn’t coming together in a lump, add flour tablespoon by tablespoon until it is.
Transfer the dough to a large, lightly oiled bowl. Cover it with a kitchen towel and let proof in a draft-free area until doubled in size, about 1 to 1 1/2 hours.
Make the rolls:Transfer the dough to a lightly floured surface and roll it out into a rectangle, about 1/2 inch (1 cm) thick, measuring approximately 12x16 inches (30x40 cm). Slice it into 12 squares. Place about a tablespoon of jam in the center of each square. Lift and pinch the opposing ends together, as if you are making a little package, to close all the openings and keep the jam inside. Gently shape them into balls.
Place the rolls in a buttered 9x13 inch (23 x 33 cm) baking pan, pinched side down. Cover with a kitchen towel and let proof for 30 minutes. Preheat the oven to 350°F (175°C).
Gently brush the rolls with melted butter right before baking (keep leftover butter for later). Bake in the center of the oven for 25-30 minutes, until the tops are brown and the rolls sound hollow when tapped.
Using the leftover melted butter, brush it over the hot rolls. Serve rolls warm or at room temperature but not hot (as the jam can burn you). Sprinkle with powdered sugar if desired.