In a stand mixer fitted with a paddle attachment, beat the butter and cream cheese until smooth. Scrape down sides of bowl. Add the sugar, salt and tomato paste, and beat until combined. You can also do this by hand.
Add the flour and mix just until dough comes together. Divide the dough into 4 pieces. Wrap in plastic wrap and place in the fridge for 1 to 2 hours, or up to 24 hours.
Preheat oven to 375 F.
Roll each piece of dough into a large circle. Using an 8- or 9-inch round, cut dough into a perfect circle. I recommend using a pizza cutter for this task.
Spread each circle of dough with 2 to 3 tablespoons of marinara sauce in a thin layer, leaving 1/4-inch border all around. Sprinkle each circle with 2 tablespoons of shredded mozzarella and press gently into sauce.
Using the pizza cutter, cut the dough into 8 even triangles. Starting at the longer end, roll up each triangle.
Place the point side down on a baking sheet lined with parchment paper or silicone baking mat.
Brush each rugelach with beaten egg and sprinkle with dried basil, dried oregano and red pepper flakes.
Bake for 16 to 18 minutes, until golden. Allow to cool on wire rack.