Gather honeysuckle flowers when they are fully open and fragrant (late afternoon or evening is when we do it).
Place the flowers in a large bowl, taking care to discard any leaves and stems. Cover with the cold water and weigh down the flowers with a plate. Let sit at room temperature for at least 12 hours.
Pour the infusion through a strainer to extract the scented water, pressing down gently on the flowers with your hands to get all of the liquid.
Heat the 1 cup of water and 2 cups sugar and stir until the sugar dissolves. Add the lemon juice, mint leaves and pinch of spicebush powder to the syrup and let boil for 4-5 minutes to form a syrup.
Let the syrup cool completely and remove the mint leaves. Add to the honeysuckle-infused water and churn in an ice-cream maker for about 20 minutes. This recipe makes about 1 quart, which can be kept in the freezer for up to a week (its flavor will diminish after that).