The many buttered layers of phyllo dough, walnut filling, and sweet syrup make baklava the ultimate special-occasion dessert in Greece.
Preheat oven to 375 degrees. In a food processor, pulse walnuts, cinnamon, and 1/2 cup sugar until finely ground.
In a medium saucepan, heat 1 cup water and remaining 1 1/4 cups sugar over medium-high; bring to a boil. Immediately reduce to a simmer; cook until slightly thickened and sugar is dissolved, 3 to 5 minutes. Remove from heat; stir in honey. Let syrup cool completely.
Brush a 12-by-2-inch round cake pan with butter. Trim each phyllo sheet into a 13-inch round (cover with plastic and a damp towel as you work). Carefully layer 7 phyllo sheets in pan, brushing butter between each layer. Sprinkle one-third of nut mixture over top. Repeat process twice more, brushing butter between each layer. Top with remaining 7 phyllo sheets, brushing butter between each layer.
Generously brush top layer with butter. Using a sharp knife with a very thin blade (such as a boning knife), cut baklava into quarters, cutting through all phyllo layers. Halve each quarter to create 8 equal wedges. Working within one wedge at a time, make two straight cuts, 1 inch apart, parallel to one side of wedge. Make two more cuts, parallel to opposite side of same wedge, creating a diamond pattern. Repeat process in remaining 7 wedges.
Bake until deep golden brown, 35 to 40 minutes. Remove from oven; pour syrup over baklava. Let cool completely before serving.