In a bowl, whisk together flour, salt, and poppy seeds. Work in butter with fingers until crumbly. Stir in cheeses. Whisk together milk and mustard; stir into flour mixture with a fork until dough forms. Shape into a 2-inch-wide log. Wrap in plastic; freeze 1 hour or up to 3 months.

Preheat oven to 350 degrees. Cut log into 1/8-inch-thick rounds; arrange on parchment-lined baking sheets and sprinkle with poppy seeds. Bake, rotating sheets once, until edges are golden, 14 to 16 minutes. Let crackers cool on a wire rack.