In a large bowl, dissolve yeast in warm water. In another bowl, combine milk, butter, sugar, salt, potato flakes and eggs. Let stand 1 minute. Add milk mixture and 3 cups flour to yeast mixture; beat until smooth. Add enough remaining flour to form a soft dough.
Turn onto a floured surface; knead until smooth and elastic, about 6-8 minutes. Place in a greased bowl, turning once to grease the top. Cover and let rise in a warm place until doubled, about 1 hour.
Place preserves, sugar, almond paste and butter in a food processor; cover and process until blended. Punch dough down. Divide in half. On a lightly floured surface, roll each portion into 14x7-in. rectangle. Spread filling evenly to within ½ in. of edges. Roll up jelly-roll style, starting with a long side; pinch seams to seal.
Place rolls, seam side down, on two parchment paper-lined baking sheets. Pinch ends together to form two rings. With scissors, cut from outside edge to two-thirds of the way toward center of rings at 1-in. intervals. Separate strips slightly; twist to allow filling to show. Let rise until doubled about 35-40 minutes.
Preheat oven to 375°. Bake for 18-22 minutes or until lightly browned. Remove from pans to wire racks to cool. Combine confectioners' sugar, vanilla and enough milk to achieve a drizzling consistency. Drizzle over warm tea rings and sprinkle with almonds.
Recipe by Bakepedia at https://www.bakepedia.com/apricot-almond-tea-ring/