Put oven rack in middle position and preheat oven to 350°F. Line a 9-inch square baking pan with foil, allowing 2 inches of foil to hang over 2 opposite ends of pan, and lightly brush foil (except overhang) with oil.
Melt chocolate with butter, sugar, and salt in a double boiler or a large metal bowl set over a pan of barely simmering water, whisking occasionally, until smooth.
Remove top of double boiler or bowl from heat and whisk in eggs and vanilla, then stir in peanuts.
Pour batter into baking pan and bake until set and edges are slightly puffed, about 15 minutes.
Transfer cake in pan to a rack to cool completely.
Beat cream cheese, peanut butter, confectioners sugar, and salt in a bowl with an electric mixer at medium speed until combined well, about 4 minutes.
Beat cream with vanilla in a bowl with cleaned beaters at medium-high speed until it just holds stiff peaks, then gently fold into peanut butter mixture until just combined.
Spread mixture evenly on top of chocolate layer and freeze, pan covered with foil, until firm, about 2 hours.
Bring cream, syrup, sugar, cocoa, salt, and chocolate to a boil in a 1-quart heavy saucepan over moderate heat, stirring until chocolate is melted. Reduce heat and simmer, stirring frequently, until thickened, about 3 minutes, then remove from heat. Stir in vanilla until incorporated. Cool sauce to warm.
Carefully lift cake from pan by grasping overhang. Trim 1/4 inch from edges of cake and discard, then cut into 8 bars. Peel off foil and serve bars with sauce.
Hot fudge sauce can be made 1 week ahead and cooled completely, then chilled in an airtight container or jar. Reheat before using. Leftover bars can be frozen, individually wrapped in plastic wrap, up to 4 days.
