Preheat oven to 350°. Beat butter and 1 1/4 cups sugar at medium speed with an electric mixer until creamy. Add cane syrup and next 2 ingredients, beating just until blended. Add eggs, 1 at a time, beating just until blended after each addition. Stir 1 1/2 tsp. ground cinnamon into flour; gradually add flour mixture to butter mixture, beating at low speed just until blended after each addition. Stir together 2/3 cup sugar and 1 Tbsp. ground cinnamon in a shallow dish or pie plate. Drop dough by rounded spoonfuls into cinnamon-and-sugar mixture, using a small cookie scoop (about 1 1/4 inches), and place 2 inches apart on parchment paper-lined baking sheets.
Bake at 350° for 8 to 10 minutes or just until edges begin to turn golden brown. Cool on baking sheets on wire racks 1 minute; transfer to wire racks. Cool completely (about 15 minutes). Store in airtight containers 1 week.