In the bowl of a stand mixer, combine the warm milk, yeast, and 1 teaspoon of granulated sugar. Stir gently and let it sit for 5-10 minutes until foamy, indicating the yeast is active.

Add the remaining 1/4 cup granulated sugar, melted butter, egg, and salt to the yeast mixture. Mix with the dough hook attachment on low speed until combined.

Gradually add the all-purpose flour, 1 cup at a time, mixing on low speed until a shaggy dough forms. Increase speed to medium-low and knead for 5-7 minutes until the dough is smooth, elastic, and pulls away from the sides of the bowl. If the dough is too sticky, add a tablespoon of flour at a time; if too dry, add a teaspoon of milk.

Lightly grease a large bowl. Transfer the dough to the bowl, turning once to coat. Cover the bowl with plastic wrap or a clean kitchen towel and let it rise in a warm place for 1-1.5 hours, or until doubled in size.

While the dough is rising, prepare the filling. In a small bowl, combine the softened butter, brown sugar, and ground cinnamon. Mix until well combined and spreadable.

Once the dough has doubled, gently punch it down and turn it out onto a lightly floured surface. Roll the dough into a large rectangle, approximately 12x18 inches.

Spread the cinnamon-sugar filling evenly over the entire surface of the dough rectangle, leaving a small border (about 1/2 inch) on one long edge. Evenly sprinkle the fresh raspberries over the filling.

Starting from the long edge opposite the border, tightly roll the dough into a log. Pinch the seam closed to seal.

Using a sharp knife or unflavored dental floss, cut the log into 12 equal rolls, about 1.5 inches thick. Lightly grease a 9x13 inch baking dish and arrange the rolls snugly in the dish.

Cover the baking dish loosely with plastic wrap or a clean kitchen towel and let the rolls rise again in a warm place for 30-45 minutes, or until puffy and almost doubled in size.

Preheat your oven to 375°F (190°C) during the last 15 minutes of the second rise.

Bake for 20-25 minutes, or until the tops are golden brown and the rolls are cooked through. If the tops start to brown too quickly, you can lightly tent the dish with aluminum foil.

Remove from oven and let cool in the dish for about 10 minutes.

While the rolls are cooling slightly, whisk together the powdered sugar, 3 tablespoons of milk or cream, and vanilla extract in a small bowl until smooth. If the glaze is too thick, add more milk 1 teaspoon at a time until desired consistency is reached.

Drizzle or spread the glaze generously over the warm raspberry cinnamon rolls. Serve immediately.