For the syrup, combine water, sugar, cranberries and peppercorns in a medium-sized sauce pan over medium-high heat. Bring to a boil and remove from heat. Cover and let stand for 30 minutes. Cool and fine-strain mixture through cheesecloth or a coffee filter into an air-tight container. Will keep refrigerated for one week, or add half an ounce of vodka to the mixture to prolong freshness up to 3 months.
For the base, combine sliced kumquats and tangerines in the base of an airtight container with ginger shrub, syrup and pavan. Refrigerate for at least two days and up to four days.
For individual servings, pour 1 and a half ounces of base into the bottom of a white wine or rocks glass along with any desired fruit from the base. Add ice cubes and top with 4 ounces of the Cava. Gently stir to combine and serve.
For a full pitcher, add the entire bottle of Cava to a pitcher containing the base. Stir gently to combine, and pour into individual serving glasses.