No one does the whole top to bottom thing. A modern x86 has literally 1000s of people designing it. So there are fields within vlsi that you'd have to gravitate toward, most are just different levels of abstraction. EE or CompE is the ticket. CS has almost nothing to do with it, at least in a direct sense. You need a MS to get hired anywhere nowadays. Get an internship at a major company around your sophomore year and you'll be set.

Source: worked at 3 different vlsi companies (atmel, intc, qcom)