Preheat oven to 350°F. Grease 13-inch by 9-inch metal baking pan. Line pan with foil; grease foil.
In large bowl, with mixer at low speed, beat butter and sugar until mixed, occasionally scraping bowl with rubber spatula. Increase speed to high; beat until light and fluffy. Reduce speed to low; beat in peanut butter, then egg until well combined, occasionally scraping bowl. Beat in flour just until evenly moistened (dough will be crumbly). Beat in peanuts. Reserve 2 cups dough.
Press remaining dough evenly onto bottom of pan. Spread jam over dough in pan. With hand, press reserved dough into large chunks (about 3/4-inch) and sprinkle over jam, leaving spaces between chunks; do not pat down.
Bake 45 to 50 minutes, until golden. Cool completely in pan on wire rack.
When cool, transfer with foil to cutting board. Cut lengthwise into three strips, then cut each strip crosswise into eight bars. Makes 24 bars.