For the sugar syrup, bring the sugar and water to a boil in a small saucepan, stirring until the sugar is fully dissolved.  Keep stirring until it reaches a boil, then remove from heat and set aside until needed.

To make the dough, start by heating the milk, butter, 1/4 cup of sugar, and the salt in a saucepan.  Stir and heat until warm (but not hot; 110 to 115 F), and the butter has mostly melted.  Set aside and let cool for a few minutes.

In a stand mixer with dough hook attachment, add 2 cups of the flour and the yeast, and give it a stir.  Turn the mixer on low and slowly add the warm milk mixture to the flour (you may need to pause the mixer to scrape down the sides). 

Add the egg as well (make sure the mixture isn't hot, you don't want to cook the egg).

Stir with the dough hook until everything is combined, then slowly add in the remaining flour until it reaches the right consistency.  For me this was just over an additional 1/2 cup (you may not need the entire amount, and you want a softer, stickier dough).

Continue to mix until the dough comes together and is shiny and smooth.  I let mine knead in the mixer for 3-5 minutes on low.

Then shape the dough into a ball and place in a large, lightly-greased bowl; turn the dough over once to grease the surface.  Cover with plastic wrap and let rise in a warm place until nearly double in size (1 1/2 to 2 hours).

Once it's doubled in size, punch the dough down and turn it out onto a *lightly* floured surface.  Cover with the plastic wrap again and let rest 10 minutes.  While it's resting, grease an 8x4-inch loaf pan.

Roll the dough into a roughly 16x12-inch rectangle.  Spread the peanut butter all around evenly, leaving a half-inch border.  Then spread the jam over the peanut butter.

Starting at the long side, carefully roll up rectangle tightly but trying not to sploosh everything out).  
Once it's rolled up, gently cut the roll in half down the length and kind of turn the filling face-up.  THIS WILL BE INSANELY MESSY, JUST GO WITH IT.

Make an "x" with the pieces. and twist each end together, keeping the messy side face-up as much as possible (you're basically going for a 2-strand "braid").

Place the crazy messy dough twist in your prepared pan, then cover and let rise in a warm place until nearly double (45 to 60 minutes).

Preheat your oven to 325°F.  Bake for 40 minutes.  

Remove from the oven and brush with the sugar syrup, then cover with foil to prevent overbrowning.  
Place back in the oven and bake another 30-40 minutes, or until golden and the bread sounds hollow when gently tapped.  The internal temperature of the bread should be 180°F to 190°F, though it's a bit difficult to tell with the filling.  I had to remove the foil for the last 10 minutes to make sure it got enough color.

Remove from the oven and again brush with sugar syrup.  Let it cool for 5-10 minutes, then loosen the loaf from the pan and carefully tip out onto a wire rack to cool completely.  Then cut and serve. If you cut it while it's still warm it will fall apart...though it's tempting.