Preheat the oven to 350º F (180º C) and line two baking sheets with parchment paper. Set aside. Note: This recipe makes about 50 wafers, so you will need two baking sheets. However, I recommend baking one tray at a time for better results.
In a medium bowl, whisk flour, baking powder, and salt. Set aside.
Using an electric hand mixer or a stand mixer, beat butter until creamy and pale on medium-high speed, about 3 – 4 minutes. Add the sugar and beat on high speed for 2 minutes until creamed and pale, scraping down the sides and up the bottom of the bowl with a rubber spatula as needed. Then add evaporated milk and vanilla; continue beating to combine, about 1 minute.
Turn the mixer to low and add the flour mixture; beat until just combined, about 30 – 45 seconds. Then add the milk; mix until well combined. Do not overmix.
Scoop dough into two-teaspoon-sized scoops and drop onto the prepared baking sheet, spacing cookies at least 2” (5cm) apart. You should be able to fit all the cookies on the two baking sheets. Note: if you don't have a small cookie dough scoop (https://amzn.to/3zwwKcr ), you can place the dough in a piping bag fitted with a medium round pastry tip. Pipe it in even mounds onto a cookie sheet (roughly 2 teaspoons).
Once all the batter has been scooped or piped, dip your fingers in some water and lightly press down on the top of each cookie to create a smooth surface.
Bake the cookies for 13 - 15 minutes, until the edges are browned. I recommend rotating the pans halfway through the bake time to ensure even browning. For cookies that remain somewhat soft in the center, aim for light browning around the edges. If you’d like a crispier cookie, bake a bit longer until the edges are golden brown.
Cool on pan 5 minutes before removing to wire racks to cool completely. Store in an airtight container at room temperature for up 5 days. If you’re going to be making banana pudding with them, I recommend leaving them out uncovered overnight, just to make them a bit stale before you use them in the pudding.