Preheat the oven to 400 degrees F.
Combine 2 cups of flour, the baking powder, and salt in the bowl of an electric mixer fitted with a paddle attachment.
Add the butter and mix on low speed until the butter is in pea-sized pieces. Mix the eggs and heavy cream and quickly add them to the flour-and-butter mixture. Combine until just blended.
Toss together the cheddar, dill, and 1/2 tablespoon of flour and add them to the dough. Mix until they are almost incorporated.
Dump the dough onto a well-floured surface and knead it for 1 minute, until the cheese and dill are well distributed. Roll the dough 3/4-inch thick. Cut into 4-inch squares and then in half diagonally to make triangles. Brush the tops with egg wash.
Bake on a baking sheet lined with parchment paper for 20 to 25 minutes, until the outside is crusty and the inside is fully baked.