Heat oven to 400°F. Put bacon on a rimmed sheet pan and bake for 15 to 20 minutes until browned and crisp; drain on paper towels.
Meanwhile, simmer tomatoes, brown sugar, vinegar and salt in a small saucepan over medium-low heat for 12 to 15 minutes, stirring, until thick enough to hold a spoon trail.
Enlarge the hole in each bottom bagel half to about 2 inches across with a small round cutter or knife, keeping the outer ring intact. Toast the cut faces of the top halves in a dry skillet for 1 to 2 minutes.
Melt half the butter in a large nonstick skillet over medium-low heat. Put two bottom bagel rings cut side down in the pan and crack one egg into each hole; cover and cook for 3 to 4 minutes until the whites are mostly set.
Turn carefully so the cut faces point up and cook for 2 to 3 minutes more until the eggs reach 160°F. Divide half the Gouda between the two bagels, cover for 30 seconds to melt and lift onto plates.
Repeat with remaining butter, bottom rings, eggs and Gouda. Put two bacon slices on each cheese-topped bottom, spread the tomato jam over the four top halves and close the sandwiches.
Rest for 1 minute before cutting; the egg should remain held in the bagel ring rather than sliding out as a separate fried egg.