Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour, salt, and baking powder in a food processor; pulse 2 times to combine. Combine 1/3 cup oil and 1/4 cup water in a small bowl. With processor on, slowly add oil mixture through food chute; process until dough is crumbly. Turn dough out onto a lightly floured surface. Knead 1 minute; add additional flour, if necessary, to prevent dough from sticking. Gently press dough into a 5-inch disk; wrap in plastic wrap, and chill at least 30 minutes.
Preheat oven to 400°.
Combine remaining 1 tablespoon oil, zucchini, squash, and garlic in a large bowl. Combine ricotta and next 6 ingredients (through egg) in a medium bowl, stirring to combine.
Unwrap dough, and roll into a 14-inch circle on a lightly floured surface. Place dough on a baking sheet lined with parchment paper. Spread ricotta mixture over dough, leaving a 2-inch border. Arrange zucchini and squash slices alternately, slightly overlapping, in a circular pattern over ricotta mixture. Sprinkle zucchini and squash with kosher salt. Fold edges of dough toward center, pressing gently to seal (dough will only partially cover squash). In a small bowl, whisk together 1 teaspoon water and egg white. Brush dough edges with egg white mixture. Bake at 400° for 40 minutes or until golden brown. Cool 5 minutes; sprinkle with basil. Cool an additional 15 minutes. Cut into 6 wedges.