Combine the yeast with the water in the bowl of a stand mixer. 

Place the milk and butter in a small saucepan over medium heat.  Heat until the milk is 100º to 110ºF. The butter does not need to be completely melted.

Add the milk mixture to the yeast mixture.  Add the sugar, salt, eggs and 3 cups of the flour.  Mix well, and continue adding flour until the mixture comes together into a smooth dough.

Switch to the dough hook and knead until smooth and elastic. Alternately, turn onto a floured surface and knead by hand for 6 to 8 minutes.  Place the dough in a greased bowl then turn once to coat. Cover and let it rise in a warm place until doubled, about 1 hour.

Make the caramel: Combine the brown sugar, butter, corn syrup, water and salt in a heavy saucepan. Bring just to a boil over medium heat. Remove from the heat.  Grease 2 9x13-inch baking dishes.  Divide the caramel between the two pans and spread evenly. (I found it was easiest to just tilt the pan until the bottom was coated.) 

Punch the dough down, then divide in half.  Roll one half into a 15x10-inch rectangle on a lightly floured surface. Spread with half of the butter and sprinkle on half of the sugar. Sprinkle half of the raspberries on top, and lightly press into the dough with your hands.  Roll up tightly, sealing the edges.  Cut into 12 equal slices and place on top of the caramel topping.  Repeat with the second half of the dough.

Cover the rolls and allow to rise until doubled, about 1 hour.

Preheat the oven to 350ºF.  Bake the rolls for 25 to 30 minutes. If the rolls start to get too brown, cover them with foil during the last 10 minutes of baking.  Remove from the oven and cool for 5 minutes before inverting onto a serving platter.