Coarsely grate the zucchini. Let it drain in a colander for 3 to 4 minutes or until you are ready to begin cooking. To hasten cooking time, squeeze the water out of the zucchini by wringing it in a clean cloth towel.
In a deep skillet, heat the olive oil/butter. Sauté the shallots or garlic briefly. Add the zucchini and toss. Cook and stir over medium to medium-high heat until the zucchini reaches a spreadable consistency, about 15 minutes. If you scorch the bottom, turn the flame down! (And scrape those delicious bits into the butter for added flavor -- you can splash in a little water to help deglaze the pan.) The zucchini will hold its bright green color and slowly caramelize into a nice vegetable jam.
Enjoy on toast, or as a side dish all summer long!