Cook the lentils according to package directions over low flame until soft (about 15 minutes), in enough cups water to cover with 1 clove of garlic. Cool, strain and set aside.
Peel the beetroots and carrots and rough chop them. In a food processor run the chopped beetroot, cloves garlic and carrots through the shredder. Or this can be done with a box grater.
In a large pot drizzle olive oil and melt the butter. Add the juice and vinegar and bring to a low simmer. Add the shredded beets, carrots and garlic. Put a lid on and simmer over medium heat for about 15 minutes to soften and bring the natural juices out of the vegetables. Remove the lid and add the spices, cooked lentils, ground almonds and a little water if needed to keep the mixture for becoming too dry. Stir well, replace the lid and allow it to cool slowly in the pan. Taste and adjust salt. Cool and puree. The filling is ready to use or transfer to a large bowl, cover and store in the refrigerator until ready to use.
Preheat the oven to 350. Place parchment paper on top of a baking sheet, or muffin tins can be used. When ready to bake the buns, roll out the bread dough after the first rise, to a long strip of dough about 8 inches wide. Spread the filling on top of the dough, leaving an inch along the long side without filling. On the other long side, begin to tightly roll the dough, jelly-roll style, until a long thin rolled dough has been formed. Cut the dough into 24 pieces. Place each piece on the prepared baking sheet or in regular size muffin tin, exposed rolled side up. Whisk the egg with a little water and brush the egg wash over the exposed rolled side.
Bake for 25 minutes or until the dough is golden brown. Once baked the filling will turn a vibrant purple color.