Position a rack in the center of the oven and heat the oven to 350°F.
Put the almonds in a 9-inch ceramic or metal pie plate and toast in the oven until pale golden, 3 to 5 minutes. Transfer the nuts to a small bowl to cool, stir in 1 Tbs. of the sugar, and set aside. Return the pie plate to the oven and raise the temperature to 425°F.
Melt the butter in a 10-inch skillet over medium-high heat. When the butter is bubbling and hot, add the plums, and cook, turning, until they begin to soften, 1 to 2 minutes. Sprinkle 3 Tbs. of the sugar over the fruit. Reduce the heat to medium low and cook until the sugar melts into the fruit juices and becomes a syrup, 1 to 2 minutes. Turn off the heat and stir in the brandy and amaretto.
In a medium bowl, whisk together the flour, salt, and the remaining 3 Tbs. sugar. Whisk in the eggs until the mixture is completely smooth; then whisk in the milk, cream, and vanilla.
Remove the pie plate from the oven and carefully butter it. Pour the fruit and syrup into the pie plate, spreading the fruit evenly.
Pour the custard over the fruit (the pie plate will be very full). Bake, sprinkling the reserved almond topping over the batter halfway through baking, until puffy and the center is set, about 15 minutes.
Let the clafoutis cool to warm, 10 to 15 minutes (it will deflate). Dust liberally with confectioners’ sugar and serve.