Combine butter, flour, and paprika in the bowl of a food processor fitted with the blade attachment. Blend until butter is cut into small pieces, about 30 seconds to a minute.
Add Cheddar and jalapeño and blend until incorporated, another 30 seconds.
Add egg yolk and blend until dough comes together. Remove dough from food processor and form into a ball. Wrap in plastic wrap then flatten into a disk. Refrigerate for at least 1 hour or overnight.
Heat oven to 350°F and line a baking sheet with parchment paper.
On a lightly floured surface roll dough into a 1/2-inch thick rectangle. Trim off edges if you want them to be perfect squares or leave edge on if you don't care about perfection.
Cut dough into 1-inch squares and place them on the prepared baking sheet. You can put them pretty close together as they really don't spread, just puff up. Poke a hole in the middle of each square with a toothpick. Brush squares with milk and sprinkle with sea salt.
Bake 20 minutes or until golden and firm.