Combine the sugar, vinegar, jalapeño, cinnamon stick, and clove in a large, heavy-duty saucepan. Cook over medium-high heat until the sugar is completely dissolved, 3 to 4 minutes.
Stir in the pears, onion, cranberries, crystallized ginger, mustard seeds, fresh ginger, and 1/4 tsp. salt. Reduce the heat to medium low, cover, and simmer, stirring occasionally, until the mixture is soft and the liquid has reduced somewhat, about 45 minutes. Uncover and continue to simmer until the liquid has almost evaporated, about 10 minutes more. Remove the cinnamon stick and clove. If you're not canning the chutney, let cool and divide among 3 clean 8-oz. jars, and refrigerate for up to 1 week.
To can the chutney:
Put three empty 8-oz. glass canning jars in a large pot of water fitted with a rack insert. The water should completely cover the jars. Cover, bring to a boil, and then turn off the heat. Put the lids in a bowl and cover with very hot water (boiling water can ruin the seal).
Remove the jars from the water and drain them. Divide the chutney among the three hot jars. Fill to within 1/2 inch of the top and wipe the edges clean with a paper towel. Screw the lids on tightly.
Return the jars to the pot of water and make sure the water covers them by at least 2 inches. Boil, covered, for 10 minutes. Use tongs to remove the jars; let them cool undisturbed on the counter. You should hear a popping sound as the jars cool, indicating that the vacuum seals have worked.