Each log makes about 45 crackers.
In a preheated 350°F oven toast 1/2 cup pecans, about 7 minutes, and cool. Finely chop toasted pecans and separate egg. In a bowl with a fork cream butter and Saga until smooth. Add egg yolk, stirring until combined well. Add flour and chopped pecans and stir until mixture just forms a dough.
Halve dough and on separate sheets of wax paper form each half into a 12- by 1 1/4-inch log, using wax paper as a guide. Freeze logs, wrapped in wax paper, just until firm, about 30 minutes.
Preheat oven to 375°F. and lightly grease 2 large baking sheets.
Cut logs crosswise into 1/4-inch-thick slices and arrange slices about 1/2 inch apart on baking sheets. Top each cracker with a remaining pecan half, pressing slightly into dough. Brush tops of crackers, including pecans, with lightly beaten egg white. Bake crackers in batches, if necessary, in upper and lower thirds of oven, switching position of sheets halfway through baking, until golden brown, about 12 minutes total. With a spatula transfer crackers to paper towels to blot and transfer to a rack to cool.