Make Vanilla Dough

1. In a bowl, combine butter, sugars and salt. Beat until smooth
2. Add eggs and vanilla, a little at a time until combined
3. Add flour and slowly mix until a dough forms, scraping down the sides at least once
4. Form dough into a log and roll with parchment paper, folding in the sides to protect dough during refrigeration. Chill the log at least 30 minutes

Make Chocolate Dough

1. Melt chocolate in microwave or over a double-boiler until smooth. Set aside to cool slightly
2. In the same bowl (there is no need to clean it), combine butter, sugars and salt. Beat until smooth
3. Drizzle in slightly cooled, melted chocolate
4. Add eggs and vanilla, a little at a time, until combined
5. Add flour and slowly mix until a dough forms, scraping down the sides at least once
6. Pat dough into a square
7. Encase with parchment and chill at least 30 minutes

Form & Chill

1. Remove both chilled doughs from refrigerator
2. Cut vanilla log in half (you will be making two separate bullseye logs when finished). Roll each half into logs about 12" in length
3. Cut chocolate dough in half. Flour work surface and roll each out to the length of the logs, wide enough to wrap the circumference of the logs, about ¼" thickness
4. Brush top of chocolate dough with egg wash (egg white + water, lightly-beaten). Place vanilla logs atop chocolate dough rectangles and roll to encase. Cut off excess dough with a paring knife. Roll with fingertips to conceal the seams in the chocolate dough
5. Roll in parchment paper and refrigerate, at least 4 hours. Logs will freeze for up to 2 weeks

Slice & Bake

1. Preheat oven to 375º
2. Line cookie sheets with parchment paper
3. Using a sharp knife or bench scraper, cut ¼" slices from log and line evenly on cookie sheets, spaced about ½" apart
4. Bake 10 minutes and let cool completely. Store in an air-tight container if not eaten immediately