Warm 1 cup milk to about 105–115°F. In the bowl of a stand mixer fitted with the dough hook, whisk together the warm milk, 2 1/4 teaspoons active dry yeast, and 1 tablespoon brown sugar. Let sit 5–10 minutes, until foamy and bubbly on top.
Melt the 6 tablespoons salted butter. Reserve a small amount of the melted butter to grease a 9×13‑inch baking dish, then add the remaining melted butter to the yeast mixture along with the 3 large eggs (room temperature), 4 cups all‑purpose flour, and 1 teaspoon salt.
Mix on low with the dough hook until the flour is incorporated, then increase speed and knead about 4–5 minutes, until the dough is smooth and elastic. If the dough is sticky, avoid adding measured extra flour; instead lightly flour your hands and the work surface to handle it.
Cover the bowl with plastic wrap or a clean towel and let the dough rise at room temperature about 1 hour, or until doubled in size.
While the dough rises, make the filling: in a small bowl combine 1/2 cup brown sugar and 1 tablespoon cinnamon. Grease the 9×13‑inch baking dish with the reserved melted butter.
After the dough has doubled, punch it down and turn it out onto a lightly floured surface. Roll the dough into a rectangle about 12 × 18 inches.
Spread 3/4 to 1 cup blueberry jam evenly over the dough, leaving about a 1/2‑inch border. Evenly sprinkle the cinnamon‑sugar filling over the jam.
Starting from the long edge closest to you, roll the dough tightly into a log. Pinch the seam to seal. Using a sharp knife or unflavored dental floss, cut the log into 12–15 equal rolls (12 for larger rolls, 15 for smaller).
Place the rolls, cut side up, into the prepared 9×13 pan. Cover loosely and let rise again at room temperature until puffy, about 30–45 minutes. Begin preheating the oven to 350°F toward the end of this rise.
Bake the rolls in the preheated 350°F oven for 25–30 minutes, until golden brown and set in the center. If they brown too quickly, tent loosely with foil for the last few minutes.
While the rolls bake, make the maple icing: in a bowl whisk together 2 cups powdered sugar, 1/4 cup maple syrup, 2 teaspoons vanilla extract, and a pinch of flaky sea salt. If you prefer a thicker icing, add up to a total of 3 cups powdered sugar; if you need to thin it, add a small amount of milk or water, 1 teaspoon at a time, until desired consistency.
When the rolls come out of the oven, let them cool 5 minutes, then spread the maple icing over the warm rolls. Sprinkle with additional flaky sea salt to taste. Serve warm.