Heat the oven to 350°F. Grease a 9x13-inch baking pan and line the bottom with parchment; lightly grease the parchment so the cake releases easily.
In a medium bowl whisk together the flour, baking powder, baking soda, salt and the 1/2 tsp ground cinnamon until evenly combined; set aside.
In a large mixing bowl, beat the softened butter and granulated sugar with an electric mixer on medium speed until pale and fluffy, about 3–4 minutes. Scrape the bowl.
With the mixer running on low, stream in the oil. Add the eggs one at a time, beating until each is incorporated. Mix in the yogurt and vanilla until smooth.
Fold the dry ingredients into the wet mixture in two additions using a rubber spatula — fold gently until just combined. Do not overmix; a few small streaks of flour are okay.
Spread the batter into the prepared pan and smooth the top. Bake on the middle rack for 30–35 minutes, or until a toothpick inserted near the center comes out with a few moist crumbs but not wet batter.
Remove the cake from the oven and let it cool in the pan on a rack for about 15 minutes. Do not remove any top layer — keeping the surface intact helps the soak absorb evenly.
While the cake cools, combine the evaporated milk, sweetened condensed milk and 1/2 cup heavy cream in a bowl and whisk until smooth.
Use a skewer or fork to poke holes all over the warm cake, going down to the pan. Slowly pour the milk mixture over the cake in three additions, allowing 5–10 minutes between pours so the liquid soaks down instead of pooling on top.
Cover the pan with plastic wrap and refrigerate for at least 6 hours or preferably overnight — this resting time is essential for the cake to become thoroughly moist and flavorful.
When ready to finish, chill the whisk and bowl for the whipped topping for 10 minutes. Beat the 2 cups cold heavy cream with the sifted powdered sugar until soft to medium peaks form, about 2–3 minutes. Spread the whipped cream evenly over the chilled cake.
Dust the top lightly with ground cinnamon and arrange sliced strawberries before serving. Keep cut slices refrigerated and serve chilled.