In a medium saucepan, combine blueberries, sugar, lemon zest, and lemon juice. Bring to a boil over medium heat, stirring constantly. Reduce to medium-low heat and cook for 8 to 10 minutes, stirring occasionally, until thick and jammy. Remove from heat and set aside to cool completely, then store in the fridge until ready to use.

In the bowl of a stand mixer, whisk together the warm milk, yeast, and ½ teaspoon of the granulated sugar. Let rest until foamy. Add the flour, remaining sugar, salt, eggs, and vanilla. Use a dough hook to knead the dough on low speed until well combined. Cover with a kitchen towel and let rest for 7 to 10 minutes.

Make a hole in the middle of the dough and add the butter in the middle, closing the dough over it. Knead the dough for 10 minutes, then cover with a kitchen towel and let rest for a few minutes. Continue to knead until the dough looks smooth and shiny and no longer sticks to the sides of the bowl.

Very lightly flour a work surface. Slap and fold the dough until smooth. Round the dough and place in a large, greased bowl, then cover with plastic wrap and let sit at room temperature for 25 to 35 minutes. Transfer the dough to the refrigerator and let rest for 2 to 3 hours (or 60-70 minutes at room temperature), until doubled in size.

After the dough rests, lightly flour a work surface and transfer the dough onto it. Divide the dough into 9 equal pieces. Roll each portion of dough into a smooth ball and place onto a prepared baking sheet. Loosely cover the buns with plastic wrap and let rest again for 30 to 45 minutes at room temperature.

In a medium bowl or base of a stand mixer, add cream cheese. Mix the cream cheese until smooth, then add lemon zest, powdered sugar, cinnamon, vanilla extract, lemon juice, and salt. Mix well by hand or with a stand mixer until smooth with no lumps of powdered sugar remaining. Set aside.

In a shallow bowl or dish, add flour, light brown sugar, and lemon zest. Stir to combine. Add cold butter and use a fork to press and cut the butter into the flour mixture until it is crumbly and it creates small clumps. Set aside.

After the dough has rested, preheat the oven to 375F.

In a small bowl, whisk together the egg and water for the egg wash.

Using the base of a glass or other round object, press the center of each of the buns to create a divot for the filling. Using a dough scoop, add a scoop of cream cheese filling to each bun. Use the back of a spoon to smooth out the filling. Then, add a spoonful of blueberry topping on top of the cream cheese. Brush the outside of the buns with the egg wash, then sprinkle with the streusel topping. Bake for 20-25 minutes, or until golden brown.

In a small bowl, add powdered sugar, vanilla extract, and milk. Stir until fully combined.

Remove the buns from the oven and allow to cool for 10-15 minutes. Drizzle with the glaze and serve with tea or coffee.