In small saucepan, bring apricots and 2/3 cup (150 mL) water to boil; reduce heat and boil gently for 5 minutes or until very soft. Reserving soaking water, drain well and transfer to food processor. Add sugar and 3 tablespoons (50 mL) of the reserved soaking water; purée until smooth, adding up to 1 tablespoon (15 mL) more water if necessary. (Make-ahead: Refrigerate in airtight container for up to 5 days.)
Preheat oven to 325ºF (160ºC).
In food processor, blend together cream cheese, cottage cheese and sugar. Blend in eggs, 1 at a time. Blend in sour cream, cornstarch, lemon rind and vanilla. Set aside.
Place 1 sheet of phyllo on work surface, keeping remainder covered with plastic wrap and damp tea towel to prevent drying out. Brush sheet with some of the butter. Place in lightly greased 9-inch (2.5 L) spring form pan, flattening against bottom into corner and scrunching top to align with rim. Repeat with second sheet of phyllo, rotating to cover side of pan completely. Brush third sheet with egg white; repeat arranging in pan. Repeat layering with remaining phyllo, brushing every third layer with egg white.
Pour one-third of the batter. Dollop one-third of the apricot purée over top; swirl with tip of knife or skewer to create marbleized effect. Repeat layers twice.
Bake in centre of oven for about 1 hour or until edge is set but centre still jiggles. Turn off oven; let stand in oven for 1 hour. Transfer to rack; let cool completely. Cover and refrigerate for at least 6 hours or for up to 2 days. Unmould and serve at room temperature.