Dissolve yeast and 1/2 teaspoon sugar in warm water in a small bowl; let stand 5 minutes. Stir in milk, 1 teaspoon vanilla, and egg. Lightly spoon the flours into dry measuring cups; level with a knife. Place flours, 1/3 cup sugar, butter, and salt in a food processor; pulse 5 times or until blended. With the processor on, slowly add yeast mixture through food chute, and process until the dough forms a ball. Process 1 additional minute. Turn dough out onto a floured surface; knead lightly 4 to 5 times (dough will feel tacky).
Place the dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until the dough is almost doubled in size. (Press two fingers into dough. If indentation remains, the dough has risen enough.)
Trim the stems off figs. Combine 1 teaspoon vanilla, figs, and orange juice in food processor; process until finely chopped. Set aside.
Punch the dough down; cover and let rest 5 minutes. Roll dough into a 15 x 10-inch rectangle on a floured surface. Spread the fig mixture evenly over dough, leaving a 1-inch margin along one long edge. Roll up the rectangle tightly, starting with the opposite long edge, pressing firmly to eliminate air pockets; pinch the seam to seal. Place the roll, seam side down, on floured surface; split roll in half lengthwise using a serrated knife. Working on a 12-inch pizza pan coated with cooking spray, coil one half of the dough, cut side up, around itself in a spiral pattern. Place the other half of dough, cut side up, at the end of the first strip, pinching the ends together to seal; continue coiling the dough to form a circle. Cover and let rise 1 hour or until the dough is doubled in size.
Preheat oven to 350°.
Bake at 350° for 30 minutes or until golden. Place cake on a serving plate. Combine powdered sugar and lemon juice in a small bowl; drizzle over hot cake. Serve warm or at room temperature.
Note: The coffeecake dough can be made ahead of time.