Pulse zucchini, bell pepper, onion and celery together in a food processor until all are in tiny pieces, scraping down sides of bowl as needed. (Do not overwork vegetables; you don't want a puree.) Transfer to a bowl and stir in salt. Let stand at room temperature for 30 minutes.
Rinse vegetables in a sieve under cold running water. Squeeze as much liquid out as possible.
Combine vinegar, sugar and spices in a large heavy saucepan and bring to a boil over medium-high heat, stirring to dissolve sugar. Stir in vegetables. Reduce heat to low and simmer, adjusting heat as necessary and stirring occasionally, until mixture is thick and liquid has evaporated, about 45 minutes. Transfer to a clean jar or dish; let cool. Cover and refrigerate until ready to use.