In a blender or food processor, finely grind 1 tablespoon almonds, 1 tablespoon flour, and 2 teaspoons sugar. Pour into a small bowl.
In a food processor or another bowl, combine 2 cups flour and 1/4 cup sugar. Add 3/4 cup butter, cut into small pieces. Whirl or rub with your fingers until fine crumbs form. Add 1/4 cup water; whirl or stir with a fork just until the dough holds together. Pat the dough into a flat disk.
On a lightly floured board, roll dough into a 15-inch-wide round, about 1/8 inch thick. Slide onto a 14- by 17-inch baking sheet; press any tears back together.
Sprinkle almond mixture onto pastry, leaving about a 3-inch rim.
Peel, core, and cut pears into 1/4-inch slices. Neatly overlap pear slices on pastry to cover almond mixture, leaving a 3-inch rim. Lift rim up and lay over pears, folding neatly to incorporate excess pastry. Sprinkle 2 teaspoons sugar and remaining slivered almonds over pears.
Melt 1 tablespoon butter (in a small pan over direct heat or in a microwave-safe bowl in a microwave oven). Brush pastry rim with butter and sprinkle with 1 teaspoon sugar.
Bake on center rack in a 400° oven until pastry is golden brown, about 40 minutes.
Slide tart onto a platter. Cut into wedges and serve hot, warm, or cool.