Vegan Lemon Bar

Cookie crust:
1/2 cup vegan butter, melted
1/4 cup granulated sugar
1 cup all-purpose flour
1/4 teaspoon salt

Lemon filling:
3/4 cup lemon juice from about 4 large lemons
optional: 2 teaspoons lemon zest
1 1/2 cups granulated sugar
1 1/4 cups full-fat coconut milk using mostly the white part
6 tablespoons of cornstarch
optional small pinch of turmeric (1/8 teaspoon) for color

For service:
powdered sugar for drizzling