Combine the grated carrots, apple, crushed pineapple with its juice, sugar, lemon juice, spices, and salt in a large heavy-bottomed pot and stir well. Place over medium heat.

Bring to a rolling boil, then reduce heat to medium-low and simmer uncovered for 35 to 45 minutes, stirring occasionally and more often as it thickens, until the jam is amber and reduced.

Test for set by dropping a spoonful onto a chilled plate. If it wrinkles when pushed, it is ready. Check with a thermometer reaching 220°F (104°C) for a soft set.

Remove from heat and stir in walnuts if using.

Ladle into clean jars, leaving 1/4-inch headspace. Wipe rims, apply lids, and cool completely before refrigerating. For shelf-stable storage, process in a boiling water bath for 10 minutes.