Sift together flour, sugar, baking powder, and salt into a large bowl. Cut in butter until it’s the size of split peas. In a separate bowl, whisk together the milk, sour cream, egg, and vanilla. Add wet ingredients to dry and stir briskly just until gathered into a sticky dough. Cover with plastic wrap and let rest for 5 minutes. Take a lump of dough slightly smaller than a tennis ball and roll it between your floured palms to form a smooth ball. Make a total of 6 balls; place them onto a greased baking sheet, brush with egg wash, and sprinkle with sugar. Bake at 425 degrees F for 15 to 20 minutes, or until golden brown. Cool on a rack and use as soon as possible.
Peel, core, and slice pears. Saute in butter, adding sugar when pears begin to soften. Cook just until tender. Spoon fruit over split shortcake biscuits and top with spiced whipped cream.