Juice 1-2 blood oranges until you have 1/4 cup of juice in total. Strain the juice, separating from pulp and seeds. Remove seeds and crush pulp to soften it.
Combine juice and pulp with coconut milk, chia seeds and diced ginger in a medium bowl.
Refrigerate overnight, up to 2 days.
Pour into individual cups and top with blood orange segments and more ginger.
Notes
You can substitute raw ginger for crystallized ginger, but may want to add 1 teaspoon of sugar.