Line 2 baking sheets with parchment paper or wax paper and set aside.
Toast the flaked coconut in a dry nonstick skillet over medium-high heat, shaking the pan frequently to ensure an even toast, until golden and fragrant, 3 to 4 minutes. Remove from the heat and allow to cool.
Add the sunflower seeds to the same skillet and toast, stirring constantly, until they are golden brown, 2 to 3 minutes. Remove and let cool.
Add the yogurt to a bowl, then add the honey and mix together. Spoon half on each of the lined baking sheets and spread out with a spatula.
Place the strawberry preserves in a piping bag, snip off the end and pipe evenly over the of yogurt. Repeat with the blackberry preserves.
Evenly sprinkle half of the strawberries, blackberries, coconut and sunflower seeds over each pan. Tap the pans on the countertop to ensure that the fruit and nuts settle into the yogurt.
Place in the freezer, uncovered, until set, at least 4 hours.
Remove from the freezer, peel off the paper and break into random pieces. Transfer to an airtight container and keep frozen until ready to eat.