Mix the flour, salt, and granulated sugar together in a large bowl. Drop the cubes of cold butter and cream cheese throughout the flour mixture. Add the vanilla to the flour mixture. Using a pastry cutter and working quickly, cut the butter and cream cheese into the flour mixture until fully incorporated and the mixture resembles a fine crumb.
If you don’t have a pastry cutter, you can also use your fingers to rub the butter and cream cheese into the flour mixture until you have a wet crumbly texture. Alternately, you can also use forks or butter knives – For this method, place one fork or butter knife in each hand and quickly cut into/mash the flour and butter/cream cheese mixture together until you have the desired texture.
Form the flour mixture into a ball and cut into four equal sections. Form each of these sections into a ball. Flatten each ball out into a flat disc and wrap tightly in plastic wrap. Store in the refrigerator for at least 3 hours or up to 72 hours (I prefer overnight).
Place the berries and sugar in a medium saucepan set over high heat. Whisk until the sugar is dissolved and the mixture begins to bubble. Lower the heat to medium and whisk in the vanilla. Simmer for 10 minutes.
While whisking the berry mixture quickly and constantly, incorporate the cornstarch. Simmer for 15 minutes, whisking often.
When the mixture has thickened, remove from the heat and whisk in the lemon juice. Pour the mixture through a fine mesh sieve into a heatproof bowl to strain out the seeds. You may need to use a rubber spatula to help stir and press the mixture through the sieve. Discard the seeds and set the jam aside to cool. If you make this mixture ahead of time, store in an airtight container in the refrigerator.
Mix all of the ingredients together in a small bowl and set aside. If you make this mixture ahead of time, store in an airtight container on the counter.
Preheat the oven to 350 degrees F and place a parchment-lined baking sheet in the freezer.
Roll out the chilled discs of dough into four 10-inch circles. Brush each dough circle with the melted butter. Next, brush 2 tablespoons of jam onto each dough circle, leaving about a ¾” edge. Next, sprinkle ½ cup of the brown sugar filling over the jam, pressing it into the jam using your hands to make sure it adheres.
Using a pizza cutter, slice each dough circle into 12 even triangles. Tightly but gently roll up each triangle, starting at the wide end and rolling towards the point.
Remove the parchment-lined sheet pan from the freezer and place the Rugelach onto the pan, leaving an inch or two in between.
Beat the egg and one tablespoon of milk. Lightly brush each Rugelach with the egg and milk mixture, being careful not to drip. Place the sheet pan back into the freezer for 30 minutes. If you need to do this in batches, make sure you are storing the uncooked Rugelach in the refrigerator and place the sheet pan into the freezer in between batches. It is important to keep everything cold – This helps keep the butter and filling from leaking out of the Rugelach during baking.
Bake the Rugelach at 350 degrees F for 15 minutes. Some of the butter and filling may leak out but this is ok! As long as it doesn’t burn, it will help caramelize the bottoms of the Rugelach. These are delicious warm or room temperature and keep well on the counter in an airtight container.