Make the cake: preheat the oven to 350 degrees F (180 degrees C). Line a 10x15 jelly roll sheet pan (also known as a Swiss cake roll pan) with parchment paper.
Sift the flour into a bowl and set aside.
Pour about 2 inches (4cm) of water into a medium saucepan and bring it to a simmer. Put the eggs, sugar and vanilla into a large bowl that fits over the saucepan without touching the water Using a hand-held mixer, beat the eggs, sugar and vanilla for at least 3 minutes until the mixture is pale, glossy and has increased in volume, with soft peaks forming.
Remove the bowl from the pan of simmering water and fold in the flour mixture a little bit at a time (at least 4 additions). Pour the batter into the parchment lined baking pan, using a spoon or spatula to gently smooth over the surface of the batter.
Bake the cake in the oven for around 10 minutes until a skewer inserted in the cake comes out clean. Remove the cake from the oven and cover it with a damp tea towel until it's completely cool.
Toast the sliced almonds. Scatter the almonds over a clean, ungreased baking sheet. Slide them in the hot oven for about 5-6 minutes until the almonds are golden brown. Watch them carefully so that they don't burn. Pull the almonds out of the oven and transfer to a plate to cool completely.
Make the whipped cream: puree the strawberries in a food processor or blender. Pour the heavy cream, powdered (icing) sugar and vanilla into a large bowl. Beat with an electric mixer until stiff peaks form, then mix in the strawberry puree, a little at a time. Stop adding strawberries if the mixture becomes too runny (you can save the rest of the puree for the strawberry sauce). Cover the bowl with plastic wrap and refrigerate at least 20 minutes.
While the whipped cream is chilling, make the strawberry sauce. Put the sugar and water in a small saucepan and bring to a gentle boil, making sure the sugar is completely dissolved. Reduce the heat to low and add the strawberries and vanilla (along with any leftover strawberry puree), and then simmer this mixture for about 4-5 minutes until the strawberries are soft. Remove the pan from heat and let cool completely.
Cut a piece of parchment paper the same size of the baking pan for the cake. Dust the surface with powdered sugar, then gently turn out the cake onto the parchment paper. Peel off the parchment paper that was lining the baking pan.
Remove the cream from the refrigerator. Using a spatula, spread a layer of whipped cream over the entire surface of the cake, saving around a cup for frosting the cake later. Drizzle some of the strawberry sauce on top of that whipped cream layer.
Roll the cake up into a log, using the parchment paper to help you shape the roll as you go. Unpeel the parchment paper from the cake roll and wrap the log in plastic wrap. Chill for at least 1 hour.
Remove the cake from the fridge after chilling and transfer it onto a plate. Frost the cake with the remaining strawberry whipped cream. Using a pastry brush, brush more strawberry sauce on the outside of the whipped cream, then use a spatula to create little ripples on the surface of the cake. Top with toasted almonds and more sliced strawberries.
Chill until ready to serve.