"Mizu shingen mochi is a Japanese water cake that is known for its delicate sweetness an evaporative texture. It takes a little practice but is well worth a little experimentation. Be careful not to overdo it with the compote. You don't want to overpower the mochi's delicate flavor."
Combine 3/4 cup hot water, 2 tablespoons sugar, and agar-agar in a saucepan; bring to a low boil. Cook and stir until sugar and agar-agar are dissolved, 3 to 5 minutes. Pour mochi mixture into a spherical mold and refrigerate until set, 6 to 12 hours.
Mix 1/4 cup white sugar and 1/4 cup water together in a saucepan over medium heat; cook and stir until sugar is dissolved, 2 to 4 minutes. Add arrowroot and stir until dissolved, about 1 minute. Add strawberries, lemon zest, and lemon juice; cook and stir over medium-low heat until strawberries soften and start to release their juice, 5 to 10 minutes. Transfer strawberry compote to a storage container and cool to room temperature; refrigerate until chilled, about 30 minutes.
Place mochi in a serving dish and drizzle strawberry compote over it.