Pouding chômeur, the Quebec maple syrup pudding cake

Ingredients

• 1 can (18 oz / 540 ml) pure maple syrup, the darkest you can find
• 3/4 cup (180 ml) heavy cream, 35%
• 1 1/3 cups (330 ml) all-purpose flour
• 3/4 cup (180 ml) sugar
• 3 teaspoons (15 ml) baking powder
• 1/2 teaspoon (2.5 ml) salt
• 1/3 cup (80 ml) cold butter, diced
• 1 egg, lightly beaten
• 3/4 cup (180 ml) milk
• 1 capful (about 1 teaspoon / 5 ml) vanilla extract