Stir together yeast and warm water in a small bowl and let stand until foamy, about 5 minutes. (If mixture doesn't foam, start over with new yeast.)
Put 1 1/2 cups flour in a medium bowl, then make a well in center of flour and add yeast mixture to well. Stir together egg, 1 tablespoon oil, and 1 1/2 teaspoons salt with a fork.
Add egg mixture to yeast mixture and mix with a wooden spoon or your fingertips, gradually incorporating flour, until a soft dough forms.
Transfer dough to a floured surface and knead, working in additional flour (up to 1/4 cup) as necessary, until smooth and elastic, about 5 minutes.
Transfer dough to an oiled bowl and turn to coat. Cover with plastic wrap and let rise in a draft-free place at warm room temperature until doubled, 1 to 1 1/2 hours.
While dough rises, heat remaining 1/3 cup oil in a 12-inch heavy skillet over medium-high heat until it shimmers, then sauté fennel seeds until a shade darker, about 30 seconds. Stir in onions, remaining teaspoon salt, and 1/2 teaspoon pepper, then reduce heat to medium-low and cover onions directly with a round of parchment paper. Cook, stirring occasionally, until onions are very tender and golden brown, 1 to 1 1/4 hours.
Preheat oven to 375°F with rack in middle.
Knead dough gently on a floured surface with floured hands to deflate. Pat out dough on a large heavy baking sheet (preferably blue steel) into a 15- by 12-inch rectangle, turning up or crimping edge, then brush mustard evenly over dough, leaving a 1/2-inch border around edge.
Spread onions evenly over mustard, then sprinkle evenly with cheese.
Bake tart until crust is golden brown, 30 to 35 minutes.
Cut into 2-inch squares or diamonds and serve warm or at room temperature.
Onion mixture can be made 2 days ahead and chilled, covered.
