Preheat the oven to 325°F . Butter a 9x5 loaf pan, line the bottom with parchment, then butter the parchment. Do not flour the pan.
In the bowl of a stand mixer fitted with the paddle attachment, combine the flour, sugar, baking powder, and salt. Mix on low for about 15 seconds.
1 cup all-purpose flour, 1/2 cup + 2 tablespoons granulated sugar, 3/4 tsp baking powder, 1/4 tsp fine sea salt
With the mixer on low, add the butter one cube at a time, then increase to medium-low. Mix for 2 to 3 minutes, until the mixture looks like wet sand.
5 tbsp unsalted butter
In a separate bowl, whisk together the oil, milk, sour cream, egg, egg yolk, and vanilla bean paste until smooth. Everything must be room temperature, or the batter will curdle.
With the mixer on low, pour in half the wet mixture and mix about 20 seconds. Scrape the bowl, add the rest, and mix 20 to 30 seconds until smooth and pourable. Do not overmix.
Pour into the pan, smooth the top, and tap it on the counter 3 times. Bake 32 to 40 minutes (start checking at 30), until a toothpick comes out with a few moist crumbs.
Cool in the pan 15 minutes, turn out, peel the parchment, and cool completely before cubing.
Macerated Strawberries
While the cake bakes, toss the diced strawberries with the sugar, salt, and lemon juice.
1 3/4 pounds strawberries, 1/3 cup granulated sugar, pinch of salt, 1 teaspoon lemon juice
Let sit at room temperature at least 30 minutes, stirring once or twice, until juicy and syrupy.
Vanilla Bean Whipped Cream
Fit the mixer with the whisk attachment. Add the cold cream, powdered sugar, and vanilla bean paste.
2 1/2 cups heavy whipping cream, 1/3 cup powdered sugar, 1 tablespoon vanilla bean paste
Start on low, then increase to high. Whip to medium-stiff peaks that hold their shape, about 1 minute. Stop before it turns grainy.
(Make-ahead option) For stabilized cream, bloom the gelatin in cold water, microwave a few seconds until liquid, cool slightly, and stream it in as you whip to stiff peaks. Or fold in cold mascarpone as you whip.
Assembly
Cut the cooled cake into bite-sized cubes.
In each glass, layer whipped cream, then cake cubes and then strawberries with some of their juice. Repeat the layers.
Finish with whipped cream and a strawberry on top. Serve cold.
Notes
Cake can be baked 2 days ahead and wrapped at room temperature. Strawberries can be macerated a day ahead. For assembled cups made more than 2 hours ahead, use the stabilized whipped cream option.