Preheat the oven to 350°F Lightly grease (or line with parchment) one large (about 18" x 13") baking sheet.
In a medium-sized bowl, beat the butter, sugar, salt, vanilla, and baking powder until the mixture is smooth and creamy. Beat in the eggs; the batter may look slightly curdled. At low speed of your mixer, add the flour, stirring until smooth; the dough will be sticky.
Plop the dough onto the prepared baking sheet. Shape it into a log that’s about 14" long x 2 ½" wide x ¾" thick. Straighten the log, and smooth its top and sides; a wet spatula or wet bowl scraper works well here. Note: For extra-long, bistro-style biscotti, pat the dough into a lightly greased 12" x 5 1/2" biscotti pan.
Bake the dough for 25 minutes. Remove it from the oven, and allow it to cool on the pan anywhere from 10 to 25 minutes; just work it into the schedule of whatever else you’re doing in the kitchen. Using a spray bottle filled with room-temperature water, lightly but thoroughly spritz the log, making sure to cover the sides as well as the top. Softening the crust just this little bit will make slicing the biscotti much easier.
Reduce the oven temperature to 325°F Wait another 5 minutes, then use a serrated knife to cut the log crosswise into 1⁄2" to 3⁄4" slices. Or cut the biscotti on the diagonal—for fewer, longer biscotti. As you’re slicing, be sure to cut straight up and down, perpendicular to the pan; if you cut unevenly, biscotti may be thicker at the top than the bottom, and they’ll topple over during their second bake.
Set the biscotti on edge on the prepared baking sheet. Return the biscotti to the oven, and bake them for 25 to 30 minutes, till they feel very dry and are beginning to turn golden. They’ll still feel a tiny bit moist in the very center, if you break off a piece; but they’ll continue to dry out as they cool. Remove the biscotti from the oven, and transfer them to a rack to cool.
Variations: Add up to 2 cups nuts, dried fruit (dried, not fresh), or chips to the dough, along with the flour. Adjust the spice to suit the add-in, if desired; e.g., add 1 teaspoon cinnamon with 1 cup chopped dried apple and 1 cup diced pecans. Or substitute hazelnut, butter-rum, or your favorite flavor for the vanilla. A classic Italian anise biscotti is made with 1/2 teaspoon anise extract (or 1/8 to 1/4 teaspoon anise oil, to taste), and 1 tablespoon fennel seeds.