In a food processor combine the flour, salt, eggs, oil and 1/4 cup water; process until dough begins to form a ball. Add more water, only if needed, 1 teaspoon at a time. Process 30 seconds more to knead. Remove dough from processor and rest, covered with inverted bowl, at room temperature for 1 hour.
Divide dough into 4 pieces. Set rollers of pasta machine at widest setting. Flatten 1 piece of dough into a rectangle (cover other pieces with inverted bowl). Lightly dust rectangle with flour and feed through rollers. Fold rectangle in half and feed through rollers 6 to 8 more times, folding in half each time and dusting lightly with flour to keep it from sticking to machine. Turn dial down one notch and feed the dough to last setting. Repeat with other 3 pieces.
Cut sheets of dough into equal lengths. Cover surface of one sheet with fresh herb leaves (stems removed). Top with second dough sheet. With lightly floured rolling pin, roll dough sheets to seal. With pastry wheel or knife, cut dough into large shapes and dust very lightly with flour. Transfer to parchment lined baking sheet and dry slightly.