Stir yogurt and cinnamon in medium bowl to blend. Cover and chill at least 1 hour and up to 1 day.
Cook orange peel in boiling water 5 minutes. Drain and reserve peel.
Melt butter in medium skillet over medium heat. Whisk in sugar. Add apricots; toss. sauté until beginning to brown in spots, about 8 minutes. Add 1 cup orange juice and reserved orange peel. Simmer uncovered until juice is reduced to thick syrup and apricots are tender, stirring occasionally, about 8 minutes. DO AHEAD Can be made 1 day ahead. Cover; chill. Bring to simmer before continuing.
Add Cognac to simmering apricots; ignite with long match. Let flames subside, shaking skillet occasionally. Mix in remaining 2 tablespoons orange juice and simmer 1 minute, stirring.
Spoon chilled yogurt into 6 dessert dishes. Spoon warm apricots and syrup over. Sprinkle with pistachios and mint.
