Puree the 450 grams of hulled strawberries in a blender or food processor until smooth. Transfer the puree to a medium heavy-bottomed saucepan and bring it to a gentle simmer over medium heat. Reduce the heat to medium-low and cook for 18 to 22 minutes, stirring and scraping more often as it thickens, until exactly 180 grams remain. The puree should leave a brief trail when stirred. Scrape it into a shallow dish and refrigerate for 25 minutes, or until completely cool.
Heat the oven to 350°F, or 175°C, with a rack in the center. Line a standard 12-cup muffin pan with paper liners. Sift the cake flour, baking powder, and 1/2 teaspoon salt through a fine-mesh sieve into a medium bowl, then whisk to distribute the leavener. In a second bowl, whisk 120 grams of cooled strawberry reduction with the room-temperature milk until uniform. Keep the remaining 60 grams of reduction chilled for the frosting.
Place the 85 grams of softened butter and granulated sugar in the bowl of a stand mixer fitted with the paddle. Beat on medium speed for 3 minutes, scraping the bowl once, until pale and creamy with fine air pockets. Beat in the oil for 30 seconds. Add the eggs one at a time, mixing for about 30 seconds after each and scraping thoroughly. Mix in 1 teaspoon vanilla. The mixture should look smooth and cohesive, not curdled or greasy.
Run the mixer on low and add one-third of the flour mixture, mixing only until most streaks disappear. Add half of the strawberry-milk mixture, followed by another third of the flour. Repeat with the remaining liquid and flour. Stop as soon as only a few dry streaks remain, then fold with a flexible spatula, scraping the bowl’s bottom and sides. The finished batter should be smooth, medium-thick, and scoopable. Vigorous mixing at this stage would toughen the crumb.
Divide the batter among the 12 liners using a scale, large cookie scoop, or piping bag, placing 55 to 58 grams in each. The liners should be approximately two-thirds full; avoid adding extra batter because it can spread over the pan instead of forming neat domes. Bake for 18 to 21 minutes, rotating the pan after 14 minutes if the oven browns unevenly. The tops should spring back lightly, and a center tester should show moist crumbs but no wet batter.
Cool the cupcakes in the pan for 5 minutes, then transfer them carefully to a wire rack and let them cool completely for about 45 minutes. For the frosting, beat the 170 grams of softened butter with the paddle on medium speed for 2 minutes until smooth. Add the confectioners’ sugar in three additions on low speed. Mix in the remaining 60 grams of cold strawberry reduction, 1/2 teaspoon vanilla, and 1/8 teaspoon salt, then beat on medium for 90 seconds until creamy and pipeable.
Fit a piping bag with a large round or open-star tip and fill it no more than two-thirds full with the strawberry frosting. Pipe one even spiral onto each completely cooled cupcake, keeping the tip about 1/2 inch above the surface so the frosting settles without tearing the crumb. If the frosting softens while piping, refrigerate the filled bag for 10 minutes. Serve once the buttercream feels creamy rather than cold and firm.