In a medium-sized pot on low heat, bring milk to a simmer and add poppy seeds, sugar, and honey.
Simmer for 15 minutes, stirring frequently until the poppy seeds absorb the milk and you have a thick paste.
Remove from heat and stir in butter and vanilla.
Place the whole mixture in the blender and blend until smooth.
Refrigerate for about 20 minutes to let the filling firm up.
Notes
If you are able to find ground poppy seeds or have a poppy seed grinder and can grind your own, feel free to substitute them for the whole poppy seeds. You will need 5 1/4 ounces, or 150 grams. You can probably also skip the blender step at the end if the resulting paste is smooth enough.Poppy seeds go rancid really quickly - they have a very high oil content. If you have any extra poppy seeds from this project, be sure to store them in the freezer.