Make the clarified butter: Melt the butter in a small saucepan over medium-low heat and cook until the bubbling starts to slow down; remove from the heat and let cool. Skim the white foam off the surface and discard. Spoon the remaining butter into a bowl, discarding the solids at the bottom of the saucepan.
Whisk the egg white, cream cheese and 1/4 teaspoon pepper in a medium bowl until smooth. Gently fold in the blue cheese and candied pecans with a rubber spatula.
Lay out 1 sheet of phyllo on a large cutting board or work surface with a long side in front of you. (Keep the remaining phyllo covered with a slightly damp towel to prevent it from drying out.) Brush the phyllo lightly with some of the clarified butter. Sprinkle evenly with 2 teaspoons breadcrumbs. Repeat to make 5 more layers (phyllo, clarified butter, breadcrumbs), stacking the phyllo as you go. (Reserve some clarified butter to brush on the strudel before baking.)
Spoon the cheese mixture in a strip down the length of the phyllo, about 1 inch from the long side closest to you. Starting from that side, roll up the phyllo to make a thin log. Wrap the log in plastic wrap or cover with a towel and refrigerate until the filling is firm, at least 1 hour.
Position a rack in the lower third of the oven and preheat to 400 degrees F. Place the phyllo roll seam-side down on a parchment-lined baking sheet. Brush all over with the remaining clarified butter. Sprinkle with pepper. Bake, rotating the pan halfway through, until the phyllo is crisp and golden brown, about 25 minutes. Let cool about 15 minutes, then transfer to a cutting board to slice. Lightly drizzle the slices with honey and serve warm or at room temperature.
Clarified butter is best for strudels: It's pure butterfat (the water and milk solids are removed), so it won't make the dough soggy.