Combine 2 cups ground poppy seeds and 1 ¼ cup milk in a medium saucepan.
Bring to a boil over medium heat, uncovered, stirring occasionally so the milk and poppy seeds do not burn. Stir in ½ cup granulated sugar, 2 Tablespoons jam, ¼ teaspoon ground cinnamon, and ⅛ teaspoon ground cloves.
Reduce the heat to medium-low and cook, stirring often, until the sugar dissolves and the poppy seeds soften, about 10 minutes. If the seeds absorb all the milk, add a splash more; as it cooks, the liquid evaporates and the filling thickens.
Stir in 1 Tablespoon rum. Transfer the filling to a bowl and let it cool to room temperature before using.
Notes
Makes about 2 cups of filling.
Use ground, not whole, seeds. Whole poppy seeds will not soften into a filling. Grind them dry, in small batches, in a poppy seed mill or clean coffee/spice grinder. Pulse in short bursts so they do not turn to oily paste. Do not use a food processor.
Pre-ground poppy seeds? Use about 1¼ cups ground for every 1 cup whole seeds. Always check they are fresh — rancid seeds taste bitter and will spoil the batch.
Done = easily spreadable, paste-like, thick and cohesive, with no liquid separating. It looks loose in the pan but thickens as it cools, so let it cool fully before judging.
Always use the filling at room temperature, never hot. Hot filling can kill the yeast in yeast dough (so it will not rise) and soften butter-rich doughs. Cool it down, or bring it up from the fridge, before filling pastries.
Too thin? Cook uncovered to evaporate liquid, or stir in a little of any of these to thicken: crushed piškoty / plain wafers (Nilla Wafers), Cream of Wheat (krupička) cooked a few minutes more, or grated gingerbread (perník). Too thick? Stir in a little milk or cream.
Storage: keep cooled filling in an airtight container in the fridge for a few days, or freeze in small portions. Flavor is best fresh.
Tip for filling: When you are filling smaller pastries like Czech kolache or kolacky, spoon the filling into a piping bag first and pipe it neatly onto the dough. It is much tidier than using a spoon, and you get an even amount in every one.