Combine the quartered strawberries, 1 cup of water, and 1/4 cup of granulated sugar in a medium saucepan. Bring the mixture to a simmer over medium heat, stirring occasionally, until the strawberries are soft and begin to break down, about 8-10 minutes.

Remove the saucepan from the heat. Add the lemon juice. Use an immersion blender to purée the mixture directly in the saucepan until smooth, or carefully transfer it to a regular blender to achieve the same consistency. Blend until completely smooth.

In a small separate bowl, whisk together the cornstarch with 2 tablespoons of cold water until a smooth slurry forms. Stir this cornstarch slurry into the strawberry purée in the saucepan. Return the saucepan to medium heat and cook, stirring constantly, for 2-3 minutes, until the soup thickens slightly. Be careful not to boil vigorously. Remove from heat and allow to cool slightly.

In another small bowl, whisk 2 teaspoons of matcha powder with 2 tablespoons of hot water until a smooth, bright green paste forms. Ensure there are no lumps.

Gently fold the matcha paste into the slightly cooled strawberry soup. Stir until fully combined and the soup has a marbled or uniformly green-pink hue. Taste and adjust sweetness if desired. For an exceptionally smooth soup, strain it through a fine-mesh sieve at this stage.

Stir in the full-fat coconut milk for added creaminess and richness. Transfer the soup to a suitable container, cover, and chill in the refrigerator for at least 1 hour, or until thoroughly cold.

Preheat your oven to 350°F (175°C). Line a small baking sheet with parchment paper.

In a medium bowl, combine the all-purpose flour, 1/4 cup of granulated sugar, 1 teaspoon of matcha powder, and a pinch of salt. Whisk these dry ingredients together thoroughly.

Add the cold, cubed butter to the dry mixture. Using your fingertips or a pastry blender, work the butter into the flour mixture until it resembles coarse crumbs. Avoid overmixing; the texture should remain crumbly.

Spread the prepared crumbs evenly in a single layer on the lined baking sheet. Bake for 10-12 minutes, or until the crumbles are lightly golden around the edges and fragrant. Keep a close eye on them to prevent the matcha from burning.

Remove from the oven and let the crumbles cool completely on the baking sheet. They will become crisp as they cool. If you prefer finer crumbs, you can pulse them briefly in a food processor once cooled.

Ladle the chilled Strawberry Matcha Soup into individual serving bowls.

Garnish each serving generously with the prepared Matcha Cookie Crumbles. Serve immediately and enjoy the unique combination of flavors and textures.