In a small bowl, combine warm water, warm milk, a portion of the sugar, and yeast. Let stand until foamy, about 5–10 minutes.
In the bowl of a stand mixer, whisk together all-purpose flour, remaining sugar, and kosher salt. Add the yeast mixture, melted butter, eggs, and vanilla extract to the dry ingredients.
Using the dough hook attachment, mix on low speed until the dough comes together. Increase speed to medium-low and knead until smooth and elastic, about 7–8 minutes.
Transfer the dough to a lightly oiled bowl, cover, and let rise in a warm, draft-free place until doubled in size, about 45 minutes to 1 hour.
For the topping, beat softened butter and powdered sugar in a stand mixer until combined. Add egg yolk and vanilla extract; mix until incorporated.
In a separate bowl, whisk together flour, baking powder, kosher salt, and freeze-dried strawberry powder. Gradually add the dry ingredients to the butter mixture, mixing until a dough forms.
Shape the topping dough into a log, wrap in plastic wrap, and refrigerate until firm, about 30 minutes.
Punch down the risen dough and let it rest for 10–15 minutes. Divide the dough into equal portions and shape each into a smooth ball. Place on parchment-lined baking sheets, spacing them apart.
Divide the chilled strawberry topping into equal portions. Roll each portion between two sheets of parchment paper into a circle large enough to cover a dough ball.
Place a topping circle over each dough ball, gently pressing to adhere. Use a sharp knife to score the topping with a shell-like pattern.
Cover the assembled conchas and let them rise in a warm place until puffed, about 30 minutes.
Preheat the oven to 350°F (175°C). Bake the conchas for 12 minutes, or until the topping is just beginning to brown and an instant-read thermometer inserted into the center registers at least 190°F (88°C).
Cool slightly before serving. Store leftovers in an airtight container at room temperature for up to 2 days.