Apple Pie, Swedish Impossible (Appelpaj)

Ingredients

• Butter (for greasing pan)
• 1/8 to 1/4 cup granulated sugar (depending upon tartness of apples)
• 1 tbsp. ground cinnamon
• Dash of ground cardamom
• 6 Granny Smith apples (about 1-3/4 to 2 pounds)
• 12 tbsp. (6 oz.) butter
• 1 cup granulated sugar
• 1 cup unsifted all-purpose flour
• 1/2 cup (2 oz.) coarsely chopped pecans (optional)
• 1 large or extra-large egg, well-beaten