Preheat oven to 350°F (180°C).
Lightly oil a baking sheet or line with parchment paper. In a medium-size bowl, use a fork to stir flour with cinnamon, nutmeg, allspice, salt, ginger and baking soda. In another bowl, use an electric mixer to beat butter with sugar for about a minute.
Beat egg and vanilla into butter mixture, then gradually beat in milk. Don’t worry if it separates. Using a spoon, gradually stir in flour mixture, then glacé mixed peel, nuts and orange peel.
Using wet hands, form dough by rounded teaspoonfuls (7 mL) into rounds, each about 1 inch (2.5 cm) wide. Place on baking sheet, a generous distance apart. Bake in centre of oven until cookies are golden, 14 to 16 minutes. Remove from oven and leave on baking sheet for 2 minutes. Remove to a rack to cool. Repeat with remaining dough. Once cooled, these cookies will keep in an airtight container at room temperature for about 5 days or in a freezer up to a month.