Add tomato paste and water to a small saucepan over medium heat. Whisk until fully smooth with no streaks.
Add vinegar, sugar, corn syrup, and salt. Whisk to combine.
Mix all spices together in a small bowl before adding. Add to the pan and whisk in.
Bring to a low simmer over medium heat, stirring frequently. You want bubbles breaking the surface consistently, not a rolling boil.
Reduce heat to low-medium. Simmer uncovered for 15 to 18 minutes, stirring every 3 to 4 minutes. The mixture should coat the back of a spoon and drip slowly rather than pour. Volume should reduce by roughly 20%.
Remove from heat. Let cool 5 minutes.
Immersion blend for 30 to 45 seconds. This is not optional. It breaks down the celery seed and creates the glossy uniform consistency Heinz has.
Cool to room temperature before jarring. The ketchup will thicken noticeably as it cools.