I have seen some similar questions, but I don't think my problem is that I have overlapping faces. I have also tried adjusting the lighting level but the problem persists. When cycles render preview does 1 or 2 out of the 32 render cycles then the coffee looks more or less correct but the end result is always grey and white and washed out. I might be able to fix this with an overlay of color in the nodes, but is there any way to avoid the problem in the first place?
render preview
blend file https://drive.google.com/file/d/17M1Bm2xdQxLtuhR7DOEmqay4WGezRiSE/view?usp=sharing
UPDATE: I turned the light intensity down and changed to darker base colors for world and sun light sources. I changed the base color of glass and coffee which improved the glass slightly, but the coffee is still ridiculously reflective. I have roughness at .5 and turning it up to 1 does not help.
Final result after applying instructions in checked answer
and after adding a transparent BSDF and decreasing transmission and increasing roughness of glass
I also decreased the light intensity for world and both lights to .4 for world and about 100 watts for each light down from 600
Final version -- https://drive.google.com/file/d/1z5UkbsWIKdtGmvthzcef6k3zenHixaNm/view?usp=sharing