Add the prepared tomatoes, celery, onions, bell peppers, jalapenos, and garlic to a large sauce pot.

Bring the pot to a simmer over medium-low heat and cook until the vegetables are soft, about 10 to 20 minutes. Stir occasionally to prevent sticking.

Once the vegetables are soft, turn off the heat and let it cool slightly, and then blend the vegetables using a food mill, food strainer, blender, food processor, or handheld stick blender. Return the mixture to the large pot.

Bring the blended sauce to a simmer over low heat and cook until the volume reduces by half, about 1 hour. Stir occasionally to prevent sticking.

While the sauce is simmering, add the peppercorns to a spice bag or coffee filter, tie it off and set aside.

Combine the brown sugar, powdered mustard, paprika, salt, and cayenne pepper in a small bowl and set aside.

Once the sauce is reduced by half, add the spice bag, brown sugar mixture, hot sauce, and vinegar to the pot.

Stir to combine and continue simmering until the mixture thickens to the consistency of catsup, about 1 to 2 hours or longer. Stir occasionally to prevent sticking.

Wash the canning jars, lids, screw bands, and tools in warm, soapy water and rinse well under clean water.

Place the canning rack into the water bath canner, place the jars in the canner, and add water to cover. Bring the canner to a simmer (180˚F) for 10 minutes, and keep the jars warm until you are ready to fill them.

Spread a dry kitchen towel on the counter. Remove a jar from the canner with the jar lifter, drain it, and place it on the towel. Keep the remaining jars in the canner so they stay hot.

Run the bubble popper through to release any trapped air, then wipe the rim with a clean, damp towel to remove any residue.

Center a lid on the jar, place the band over it, and screw it on until fingertip tight. Place the jar back into the canner, and repeat with the rest of the jars.

Once the filled jars are all in the canner, adjust the water level so it is at least 2 inches above the tops of the jars.

When the processing time is complete, turn off the heat, and let the canner cool and settle for about 5 minutes.

Spread a dry kitchen towel on the counter. Carefully remove the cover by tilting the lid away from you so steam does not burn your face.

Use the jar lifter to remove the hot jars from the canner and place them on the towel.

Let the jars sit undisturbed for 12 to 24 hours to cool. Don't tighten bands or check the seals yet.

After 12 to 24 hours, check to be sure the lids are sealed by pushing on the center. The cover should not pop up. If the top flexes up and down, it failed to seal. Refrigerate the jar and use it up within a week.

Remove the screw-on bands and wash, label, and date the jars. Store the barbecue sauce in a cool, dark place and use it within 18 months for the best quality. After opening, store any leftovers in the refrigerator and use up with a week. Yields about 8 half-pint or 4 pint-size jars.