Preheat the oven to 375°F. Line a baking sheet with parchment paper, then set aside.
For the sausage: cook in the oven to an internal temperature of 160°F using a thermometer.
In a bowl, combine flour, sugar, baking powder, and salt. Mash the butter in with a fork or your fingers until its crumbled in fine. Gently stir in the milk until a semi sticky dough forms. Portion the dough evenly into round discs (lightly flour the dough if needed, try not to handle it very much) onto the prepared baking sheet. Place into oven and bake for about 15 minutes, or until cooked in the center (toothpick inserted should come out clean). Let cool for 5 minutes before serving. Cut in half and butter if desired.
Fill a saucepan halfway with water. Bring the water to a simmer. Stir the vinegar into the water. Crack the eggs into a bowl to make sure the yolks dont break. Stir the simmering water in a circular motion then gently place the eggs into the water. (You can poach multiple eggs at once, being careful not to overcrowd the pan.) Cook the eggs in the water for 3-5 minutes, gently flipping over about halfway through until the whites are firm. Remove the eggs with a slotted spoon onto a paper towel to drain excess water. Season with salt and pepper.