Good morning. Shall I serve you some rice?

Literal

Good-morning. Rice [obj-を] serve-[permission-ても] good [feminine-かしら]?

よそう (装う/盛る) 'to serve rice into a bowl / to dish up' is the standard kitchen verb for portioning rice. かしら is a feminine sentence-final particle expressing wonder or gentle questioning — 'I wonder if / shall I?' The combination is a quintessential domestic morning scene.