Heat oven to 400°F. Bake bacon on a rimmed sheet 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 12 to 15 minutes, stirring, until a spoon leaves a trail.
Widen each bottom bagel hole to about 2 inches with a small cutter or knife, keeping outer ring intact. Toast top halves cut-side down in a dry skillet 1 to 2 minutes.
Melt half the butter in a large nonstick skillet over medium-low. Place two bottom rings cut-side down; crack one egg into each. Cover; cook 3 to 4 minutes until whites mostly set.
Carefully turn cut-side up; cook 2 to 3 minutes more until eggs reach 160°F. Divide half the Gouda between bagels; cover 30 seconds to melt. Transfer to plates.
Repeat with remaining butter, rings, eggs, and Gouda. Top each with two bacon slices. Spread tomato jam over four top halves; close sandwiches.
Rest 1 minute before cutting, keeping eggs held inside bagel rings.