In a small pot, gently heat the cider vinegar and pickling spice.
Once warm, turn off the heat and let the spices steep for at least 45 minutes to infuse the vinegar with flavor.
While the vinegar steeps, heat the neutral oil in a large pot over medium-high heat.
Add the bell pepper, onion, celery, and garlic.
Cook, stirring occasionally, until the onion has softened, about 5-7 minutes.
Stir in the tomato paste and cook for another 1-2 minutes, allowing it to coat the vegetables and deepen in color.
Add the chopped tomatoes, stir well, and scrape any browned bits from the bottom of the pot.
Reduce the heat to maintain a gentle simmer.
Cook, stirring occasionally, for about 45 minutes, or until the mixture has started to thicken. Be careful not to let the tomatoes stick and burn.
Strain the spiced vinegar through a fine-mesh sieve directly into the tomato mixture, discarding the whole spices.
Stir in the brown sugar, a pinch of salt, and a dash of cayenne.
Continue to simmer for another 45 minutes, or until the ketchup has reached a consistency just slightly thinner than bottled ketchup (it will thicken more as it cools).
Taste and adjust the seasonings as needed—more salt, sugar, or cayenne to your liking.
Use an immersion blender to purée the ketchup until smooth directly in the pot. Alternatively, let it cool slightly and carefully blend in a countertop blender until completely smooth.
Let the ketchup cool completely.
Transfer to an airtight container or jar and store in the refrigerator for up to 2 weeks.
