Stir together breadcrumbs and 1/4 cup shredded cheese; sprinkle on the bottom of a buttered 9-inch springform pan.
Beat cream cheese at medium speed with an electric mixer; add half of ham, shredded cheese, and next 6 ingredients, beating at low speed until well blended. Pour half of cheese mixture into prepared pan; top with remaining ham. Pour remaining cheese mixture over ham.
Bake at 325° for 1 hour or until center is set. Let stand 30 minutes. Gently run a knife around the edge of cheesecake, and release sides. Serve slightly warm or at room temperature with crackers.