Brownie layer:

Put oven rack in middle position and preheat oven to 375 degrees.

Lightly butter a 13" x 9" baking pan and line with 2 crisscrossed sheets of foil, leaving a 2" overhang on all sides. Butter the foil.

(This sounds like a fussy preparation for the pan -- but really, it's worth it.)

Melt butter and chocolate with brown sugar in a 3-quart heavy saucepan over moderate heat, stirring occasionally, until smooth.

Remove from heat. Whisk in eggs and vanilla until combined. Whisk in flour, cocoa, and salt until just combined.

Spread batter evenly in baking pan and bake until set and a wooden pick inserted in center comes out with moist crumbs adhering, about 20 minutes.

Cool completely in pan on a rack, at least 1 1/2 hours.

Mint ganache:

Bring 1/2 cup cream to a simmer in a 2-3 quart saucepan and remove from heat. Pour over white chocolate in a bowl. Let stand one minute, then whisk until smooth.

Stir in créme de menthe and extract and chill, covered, stirring occasionally, until thick, about 1 hour.

Chocolate ganache:

Bring 1 cup cream to a simmer in a 2-3 cup saucepan and remove from heat. Pour over bittersweet chocolate in a bowl. Let stand one minute, then whisk until smooth.

Chill, covered, stirring occasionally, until thick, about 30 minutes.

Assemble:

Spread mint ganache over top of cooled brownie in a thin, even layer, then chill until firm but still lightly sticky, about 30 minutes.

Spread chocolate ganache over mint and chill until firm, about 2 hours.

Lift dessert out of pan using foil overhang. Run a heavy knife under hot water and wipe dry, then trim edges of dessert (1/4" off each side.) Cut dessert into squares and peel from foil.