Puree the mango flesh in a food processor or blender until completely smooth. Set aside.
Run the pineapple through a juicer, collecting both the juice and the pulp. Measure the final yield carefully.
Run the cubanelle peppers and jalapeños through the juicer. Measure the final pepper juice and pulp yield.
After juicing, go through the pulp container and discard the tough pineapple fibers, dry pulp, and larger pepper skins.
Keep the soft pulp and return it to the juice mixture.
Pour the pineapple juice and pulp, pepper juice and pulp, and mango puree into a large heavy-bottomed pot. Stir until fully combined.
Add the sugar, apple cider vinegar, bottled lime juice, smoked paprika, coriander, and cumin.
Stir until the sugar is fully dissolved and the spices are evenly distributed.
Bring the mixture to a full rolling boil over medium-high heat, stirring regularly to prevent scorching.
Reduce the heat to medium and maintain a steady simmer.
Cook for approximately 40–60 minutes total. Start checking consistency around the 40-minute mark.
The jam is ready when it thickens and passes the chilled plate test.
Stir regularly throughout cooking to prevent sticking and ensure even reduction.
As the jam cooks, skim off any foam that rises to the surface.
Once the jam reaches the proper consistency, remove it from the heat and immediately proceed with the water bath or atmospheric steam canning method.
