In the workbowl of the standing mixer, whisk together the milk, yeast, and sugar. Let proof for 5-10 minutes. Add the butter, eggs, salt, and flour. Mix/knead for 5 minutes at low speed. Then transfer the dough to a non-floured work surface, and knead it by hand until it is smooth and not at all sticky -- about 1 minute.
Form the dough into a ball, and place it in the greased mixing bowl. Flip the dough to grease the other side. Then cover the bowl with plastic wrap, and let the dough rise in a warm-ish location until doubled in volume -- about 90 minutes.
Delate the dough and transfer it to the non-floured work surface. Pat the dough into a rough rectangle. Use a rolling pin to press the dough into a 12 inch wide, 16 inch long rectangle. Spread the dough with a thin layer of the strawberry jam. Starting at the 16-inch side, tightly roll the dough into a log. Pinch the seam to seal it. Then use a sharp knife or pastry ("pizza") cutter to cut the log lengthwise in half. Crisscross the two halves (jam-side-up) and then twist into a rope. Coil the rope into a circle. Use two flat spatulas to transfer the coil to the pepared springform pan.
Spoon the remaining jam into the crevices of the pastry. Then stud the crevices with the cut up strawberries. Cover with plastic wrap, and let rise until doubled in volume -- about 45 minutes. Meanwhile, preheat the oven to 350°F.
Bake, uncovered, in the preheated oven until the bread puffs completely and its top turns golden brown -- about 30 minutes. Transfer the pan to a wire rack for 5 minutes while you mix up the glaze.
To make the glaze, whisk together the confectioners' sugar, cream or milk, and vanilla in a medium size bowl or pitcher.
Unmold the bread while it is still quite warm, and immediately pour on the glaze. Serve while warm. Leftover portions -- if there are any -- can be reheated for 30 seconds in a microwave oven.