Mix together the vegetables & layer in a large bowl. Sprinkle each layer with salt. Pour in just enough water to cover. Place a plate on top to keep the vegetables submerged. Cover & refrigerate for 8 hours or overnight. Drain, rinse in several changes of water & drain again.
Meanwhile, place 4 sprigs of basil in a small jar. Add whole garlic & just enough oil to cover. Cover tightly & refrigerate for 8 hours or overnight.
Prepare pickling brine by boiling the water, vinegar & sugar. Bring to a boil, stirring till the sugar is dissolved & then keep hot until ready to use.
Sterilize 4 500mL canning jars. In each one, place a basil sprig, garlic clove & 1/2 ts mustard seeds. Without forcing, pack the vegetables into the jars leaving 3/4" headspace. Pour pickling brine into each jar up to 1/2" of the top.
Remove any air bubbles by sliding a rubber spatula around the edge of the jar; wipe rims & fir lids. Process in a boiling water bath for 20 minutes. Remove, cool, label & store.