Jamms os

Right guys, owned this 1 series a year 99,800 on clock spent money on new water pump and stat and other bits, but when it’s cold and idle before driving off it’s so rough and shakey if I drive immediately after starting engine it’s fine but if I sit idle 2-5mins it shakes bad then the u feel a jolt and the ember engine light flashes, I switch it off and back on and it’s gone then it’s fine? Anyone experienced this