Preheat the oven to 350°F. Grease a 9×5-inch loaf pan and line the long sides with parchment paper. Toss the blueberries with 1 tablespoon of flour and set aside.
Beat the softened cream cheese, sugar, egg yolk, and vanilla until smooth. Set aside.
Whisk 1¾ cups flour with the baking powder, baking soda, and salt.
In a large bowl, whisk the melted butter and sugar until combined. Whisk in the eggs, then add the Greek yogurt, lemon juice, lemon zest, and vanilla.
Fold the dry ingredients into the wet mixture just until no large streaks of flour remain. Gently fold in the flour-coated blueberries.
Spread a little more than half of the blueberry batter in the pan. Spoon the cream cheese mixture over the center, keeping it slightly away from the sides. Add the remaining batter on top.
Run a thin knife through the batter two or three times to create a gentle swirl.
Bake for 55 to 65 minutes, until the top is golden and a tester inserted into the cake portion comes out without wet batter. Avoid the cream cheese ribbon or a large berry when testing. If the top browns before the center is done, loosely cover with foil and continue baking.
Cool in the pan for 20 minutes. Lift the loaf out with the parchment and transfer to a rack. Let it cool completely before slicing into 10 slices. Allow about an hour of cooling for planning, including the pan time; the loaf may need longer.