Preheat oven to 340°F (170°C).
Liberally butter a 9-inch cake pan. Line the bottom with a circle of parchment, then the sides of the pan with 2-inch strips; butter the parchment.
Place the almonds on a baking tray and toast them until golden, about 10 minutes. Cool.
In a large bowl, beat eggs and sugar until light and creamy. Add vanilla, butter, flour, baking powder, and salt, and mix well. Pour into the prepared cake pan.
Bake for 25 minutes, or until a wooden skewer comes out clean.
Reset the oven to 400°F (200°C).
10 minutes before the cake is done, place butter, sugar, and milk in a pot and bring to a boil. Let simmer for five minutes then add the almonds. Spread the almond mixture on top of the cake, even it out with a spatula, and sprinkle with some flaky sea salt.
Return the cake to the oven and bake the cake for another 10 minutes. The top should be bubbly and golden.
Cool briefly on a wire rack. Use a very sharp knife to cut around the edge of the cake before it is cold, as the praline topping sets very quickly.
Turn it out onto the rack to finish cooling.