Line a small baking sheet with parchment paper. Set aside.
In a small non-stick skillet heat the butter over medium heat until melted.
Add nuts, cinnamon, and honey and stir continuously until nuts are evenly coated and sticky, about 3-5 minutes. Be careful not to burn the mixture.
Using a slotted spoon or a spatula quickly remove nuts from the skillet to the baking sheet. Spread the nuts, separating them as much as you can, right away; let cool down. If necessary, use a knife to cut down larger clumps.
In a small saucepan, combine sugar, lemon juice, and water; bring to a boil.
Reduce heat and simmer until sugar dissolves and the mixture is syrupy about 10 minutes.
Set aside to cool.
Preheat oven to 350 degrees Fahrenheit.
Brush a 12-cup muffin pan with softened butter and set aside.
Place 1 phyllo sheet on a work surface and lightly brush with melted butter using a pastry brush. Repeat with 5 more sheets of phyllo, laying each on top of the other and brushing with butter.
Using a sharp knife, slice the phyllo stack into 12 equal squares.
Carefully press the phyllo squares into each buttered muffin cup, creating a ruffled phyllo cup (it doesn’t have to be perfect).
Bake until the phyllo cups are crisp and deep golden in color for about 15 minutes, keeping an eye on them towards the end to ensure they don’t burn.
Immediately pour the cooled syrup on top of each hot phyllo cup. Allow the cups to soak the syrup and cool until slightly warm.
Gently hold each cup upside down to allow any excess syrup to drip.
Transfer the phyllo cups to a wire rack placed over a baking sheet. Let the phyllo cups cool completely.
To serve, place a scoop of ice cream into the cooled cups and top with candied nuts and drizzle with honey if desired.
Fold the candied nuts into softened ice cream and then freeze again.
Substitute walnuts with pecans or use butter pecan ice cream.
Prepare nut topping and syrup several days in advance. Refrigerate the syrup.
Bake and soak phyllo cups a day ahead (keep loosely covered with foil, do not refrigerate).