Make the dough. Melt the butter, then warm the milk in the same bowl until it's slightly warm. In a stand mixer with the dough hook, combine the starter, sugar, and eggs. With the mixer on low, slowly pour in the warm milk and butter. Add the flour and salt and mix until combined - the dough will look rough and sticky, that's fine. Cover and rest for 30 minutes, then knead on medium speed for 6–8 minutes until soft and pulling away from the sides of the bowl. Transfer to a lightly oiled bowl, cover tightly, and let rise at room temperature (around 67–68°F) overnight for 8–12 hours until doubled.
Make the garlic butter. Melt the butter over medium-low heat, add the garlic and cook for 1–2 minutes until fragrant. Remove from heat, stir in the parsley, and set aside to cool slightly.
Shape the dough. Divide your fully risen dough into small balls, roughly 30–35g each.
Drench and layer. Roll each ball in the garlic herb butter, then in the parmesan, and layer into a well-greased bundt pan. Continue until all the dough balls are in the pan. Drizzle any remaining butter over the top and finish with flaky salt.
Second proof. Cover and let proof until the dough has completely doubled in size again, about 2–3 hours. This can take longer in a cooler kitchen - don't rush it. The dough should look pillowy and feel light when gently pressed.
Bake. Preheat oven to 375°F (190°C). Bake for 32–36 minutes until deep golden brown and internal temperature has reached 190F/88C. Tent with foil at the 25-minute mark if the top is browning too quickly.
Make the glaze. Beat together the cream cheese, lemon zest, powdered sugar, chives, salt, and pepper until smooth and fluffy. Then the lemon juice and beat. Next, add the warm milk a little at a time, mixing as you go, until you reach a consistency you're happy with (drizzleable but not too thin).
Finish. Cool in the pan for exactly 10 minutes, no longer, or it risks sticking to the pan. Invert onto a board and let cool before drizzling generously with the glaze and serving warm.