4 tablespoons well-chilled unsalted butter, cut into 4 pieces
Directions
Stir sugar, molasses and butter in heavy 2- to 3-quart saucepan over low heat until butter melts. Cool mixture to lukewarm.
Stir egg, vinegar and vanilla into molasses mixture. Combine 3 cups flour and next 6 ingredients and gradually stir into molasses mixture. Cover and chill 1 1/2 hours to firm. (Can be prepared 3 days ahead.)
Invert baking sheets and cover undersides with foil. Brush with melted butter and dust with flour, shaking off excess. Form dough into 1-inch balls. Arrange on foil, spacing 3 inches apart. Flatten each cookie into 3-inch round (saucepan bottom wrapped in plastic works well.) Chill 1 1/2 hours.
Preheat oven to 325°F. Bake cookies until honey colored, about 14 minutes. Slide foil onto work surface. Gently press each cookie with spatula to flatten. Cool. (Can be prepared 2 days ahead. Store in airtight container.)
Blend 1 1/4 cups sugar and 3 1/2 tablespoons ginger in processor until ginger is minced, stopping occasionally to scrape down sides of work bowl, about 2 minutes. Add 2 tablespoons marmalade and 2 tablespoons butter. Process until thick and well blended, about 1 1/2 minutes. Transfer mixture to small bowl. Repeat with remaining sugar, ginger, marmalade and butter. Add to bowl. (Can be prepared 1 day ahead and refrigerated. Bring to room temperature before continuing.)
Spread 1 tablespoon filling on bottom of cookie, smoothing to edges. Press bottom of another cookie firmly onto filling. Repeat with remaining cookies. (Can be prepared 6 hours ahead. Store uncovered to retain crispness.)
