Drain tomatoes in a fine wire-mesh strainer over a large saucepan.
Cut tomatoes in half lengthwise; using fingers, remove and discard seeds and surrounding gel.
Place seeded tomato halves in saucepan with drained juices.
Using a rubber spatula, press any remaining pulp through strainer into saucepan; discard any seeds.
Add sugar, molasses, black pepper, and salt to tomatoes.
Bring mixture to a simmer over medium-high, stirring often; reduce heat to medium.
Using a potato masher, break down tomato flesh until mostly smooth but still slightly textured, about 1 minute.
Simmer over medium, uncovered, stirring occasionally, until thickened, glossy, and reduced by half, 45 to 50 minutes.
Remove from heat; stir in vinegar and lemon zest.
Let cool completely, uncovered, for about 1 hour.
Transfer to a clean, lidded pint jar.
Keep in the refrigerator for up to 10 days.
