3 3/4 cups strained pink-grapefruit juice (from 5 grapefruits), or use unsweetened store-bought juice
2 tablespoons plus 1 1/2 teaspoons unflavored gelatin (from four 1/4-ounce envelopes)
1 cup orange segments (from 3 seedless oranges)
Bring water and sugar to a boil in a medium saucepan, stirring until sugar dissolves. Add peppercorns if desired. Refrigerate for 2 hours and strain through a fine sieve.
Prepare an ice-water bath. Stir syrup, Campari, and salt into grapefruit juice (you should have about 6 cups liquid).
Sprinkle gelatin over 1 cup juice mixture in a small saucepan, and let stand until softened, about 5 minutes. Bring to a simmer over medium-high heat, stirring until gelatin dissolves. Strain gelatin mixture through a fine sieve into remaining juice mixture in a bowl set in ice-water bath. Let stand, stirring occasionally, until mixture begins to gel, about 30 minutes.
Remove from ice water bath and pour half the gelatin mixture into a 7-cup bowl. Arrange orange segments around perimeter, pressing them into the gelatin. Refrigerate 30 minutes. (Remaining gelatin can sit at room temperature.) Pour remaining gelatin on top. Refrigerate for at least 3 hours or up to overnight.
For a slightly spicy dessert, add crushed pink peppercorns.