Prepare the dough: Whisk the warm milk, 2 Tablespoons sugar, and the yeast together in the bowl of your stand mixer fitted with a paddle attachment. Cover and allow mixture to sit for about 5 minutes or until foamy on top. *If you do not own a mixer, you can do this in a large mixing bowl and in the next step, mix the dough together with a large wooden spoon/rubber spatula or dough whisk.*
On medium speed, beat in the remaining sugar (which should be ½ cup) and the softened butter until it is slightly broken up. Add the eggs and salt and beat on medium speed until combined. The butter won't really be mixing into the mixture, so don't be alarmed if it stays in pieces. Switch the mixer down to low speed and with it running, add 1 cup of flour at a time, making sure it's fully incorporated before adding the next. After 4 cups have been added, add the last ½ cup and beat until the dough comes together and pulls away from the sides of the bowl, about 3 minutes. Dough will be soft.
Knead the dough: Switch to the dough hook attachment. Knead dough on low speed for about an additional 5 minutes (or knead by hand on a lightly floured surface for about 5-7 minutes; use additional flour as needed if dough is too sticky but be careful not to add too much). Knead dough until it is smooth and elastic. Poke the dough with your finger—if it slowly bounces back, your dough is ready to rise. If not, keep kneading.
1st Rise: Lightly grease a large bowl with oil or use nonstick spray. Place the dough in the bowl, turning it to coat all sides in the oil. Cover the bowl with aluminum foil, plastic wrap, or a clean kitchen towel. Allow the dough to rise in a relatively warm environment (on the counter is fine) until double in size, about 2 hours.
Grease the bottom and sides of a metal or glass 9x13-inch baking dish or line with parchment paper.
Roll out the dough: Punch down the dough to release the air. Place dough on a lightly floured work surface and using a lightly floured rolling pin, roll dough into a 12x18-inch rectangle. Make sure the dough is smooth and evenly thick. If the dough keeps shrinking as you roll it out, stop what you're doing, cover it lightly, and let it rest for 10 minutes to relax the gluten. When you return to the dough, it should stretch out much easier.
Make the filling: In a medium bowl, toss the frozen raspberries with the sugar and cornstarch. Spread the cold sugared raspberries evenly over the dough. Tightly roll up the dough to form an 18-inch-long log. Cut into 12 even rolls (about 1½ inches in width each). Arrange them in the prepared baking pan, cut sides up.
2nd Rise: Cover the rolls tightly and allow to rise until puffy, about 90 minutes. (Or use the overnight option in the Notes below.) The berries will release their juice at the bottom of the pan - this is OK.
Preheat the oven to 350°F (177°C).
Bake: Bake rolls for about 28–32 minutes or until they are lightly browned on top. About halfway through baking time, tent a piece of aluminum foil over the pan to prevent the tops from browning too quickly. Remove pan from the oven and place pan on a wire rack for about 10 minutes as you make the icing.
Make the icing: In a medium bowl using a handheld or stand mixer fitted with a paddle or whisk attachment, beat the cream cheese on medium speed until smooth and creamy. Add the confectioners' sugar, cream/milk, and vanilla. Beat on low speed for 30 seconds, then switch to high speed and beat for 1 minute. Spread the icing over the warm rolls and serve immediately.
Cover leftover frosted or unfrosted rolls tightly and store at room temperature for up to 2 days or in the refrigerator for up to 5 days.