Preheat the oven to 475°F (245°C) with a baking sheet. Continue to heat the oven for additional 10 to 12 minutes longer to heat the baking tray properly.

Wash, dry pat, remove apricot pits, and cut each fruit into slices about 1/2 inch (1 cm) thick. In a mixing bowl, place the softened butter, icing sugar, weighted egg, almond flour, and all-purpose flour and mix using a rubber spatula.

For shaping the pizza dough, generously dust a cutting board with regular flour. Press the dough down with your hands and spread it to the edges without using a rolling pin. Take time to stretch it into a round, approximately 10 inches (25 cm) in diameter. Make it thinner in the middle and thicker on the edges.

Spread the almond cream on the top of the dough, leaving about 1 inch (2.5 cm) around the edge. Arrange apricot slices on top, slightly pressing them down. Sprinkle the pizza with the toasted flaked almonds.

Use the oven mitts to take the hot baking sheet from the oven carefully. Coat it with olive oil (or any other oil) using a silicone brush. Slide the pizza dough onto the greased baking tray. If you prefer, you can also use a metal pizza peel.

Bake the pizza on the middle rack of the oven for 10 to 15 minutes until it is golden brown. Use oven mitts to take it out and move it to a cutting board with parchment paper. Cut the pizza using a large knife or a pizza cutter.