Combine yeast, warm water, and 1 teaspoon sugar in a glass measuring cup. Let stand for 5 minutes.
Using an electric mixer, beat 1/2 cup butter at medium speed until creamy. Gradually add 1/2 cup granulated sugar and salt. Beat until light and fluffy.
Add eggs one at a time, beating to incorporate. Add milk and lemon juice and beat until blended.
With mixer on low, add yeast mixture. Gradually add the 4 1/2 cups bread flour and then add the nutmeg. Beat on low speed 1 to 2 minutes.
Sprinkle about 1/4 cup flour on a flat surface. Place dough on surface and knead until smooth and elastic, about 5 minutes. You can add a little extra flour if necessary to keep dough from sticking to your hands and the surface.
Lightly grease a large bowl with vegetable oil and place dough in bowl. Turn dough so that all sides are coated in oil. Cover with a clean dish cloth and let rise in a warm (85 degree) place, free from drafts, for 1 1/2 to 2 hours or until doubled in size.
Punch dough down and place on a lightly floured surface. Roll into a 16X12-inch rectangle.
In a small bowl, mix together 6 tablespoons butter and strawberry jam. Spread on dough. Sprinkle with brown sugar and scatter sliced strawberries across dough.
Starting at one long end, roll up jelly-roll style. Cut into 14 slices and place in 2 lightly greased round cake pans.
Cover and let rise in a warm place for 1 hour, or until doubled in bulk. You can also refrigerate overnight and let rise in the morning for about 1-2 hours. If you do this, there will most likely be liquid from the strawberries in the bottom of the pan. Pour out about 1/2 of the liquid so that the rolls will not get soggy as they bake.
Preheat oven to 350 degrees and bake for 20 to 22 minutes, until golden brown. Let rolls cool slightly before adding cream cheese drizzle
To make cream cheese drizzle, beat cream cheese on medium speed with an electric mixer. Gradually beat in powdered sugar. Mix in both extracts and milk.
Use a spoon or a ziptop bag with the corner clipped to drizzle on sweet rolls.