Melt the butter in pan, add sugar and water just until the sugar is dissolved, whisking the whole time Add the milk and stir.
In the bowl of an electric mixer, place 2 cups of Einkorn flour and the yeast. Mix briefly with the whisk attachment.
Add vanilla. Slowly pour liquids over the flour in the mixer. Add the egg. Mix briefly.
Add salt, and remaining flour ½ cup at a time.
Once flour is well combined, switch to the dough hook and mix on low for 3-5 minutes. Dough should bounce back when pressed and not stick to your finger.
Transfer dough to greased bowl, cover with cling wrap. Allow to rise for 25 minutes.
After first rising, separate dough into 2 balls. Working with one ball at a time, roll each section into a long rectangle. Keep the dough about ¼ inch thick.
Combine filling ingredients into a bowl and mix until well combined. Spread over dough in an even layer.
Roll dough the skinny way if you want smaller rolls, and the thick way if you want fewer, larger rolls.
Slice roll into 1 ½ inch sections and place in a greased pan, cover with a towel for second rising. Let rise for an hour and a half.
Bake at 350° for 15 – 20 minutes, or until golden brown.
Once baked, allow to cool slightly (if you can) and drizzle with finished icing.
Mix powdered sugar, cream cheese, milk, and vanilla together until smooth. Drizzle over rolls and serve warm.
IF MAKING AHEAD:Freeze or refrigerate after shaping the rolls, don't allow them a second rise. Thaw the night before, if removing from the freezer. Let sit at room temperature for about 30-45 minutes before baking. Bake and ice as normal.