Obviously got the Mdf cut then exactly what process do you do of you don't mind ?
1. Get MDF cut.
2. Assemble into your cupboard, cut holes, bolt together, fill hole, repair any damage etc.
3. Use roller to prime with MDF primer (or can use very diluted white emulsion paint), but MDF primer is designed to do the job and does a better job than dilute emulsion.
4. Use rollers like these
B&Q Mini Roller Gloss Sleeve Refills, Pack of 10, 0000003765135
5. Throw away roller and tray after use.
6. Sand with extremely fine sand/flour paper.
7. Second primer coat and/or filling might be required.
8. I rollered on thinned emulsion paint. (maybe adding 10-20% water).
9. Let dry & sand with extremely fine sand/flour paper.
10. Second or third coat will/may be needed.
11. Let dry & sand with extremely fine sand/flour paper.
12. Roller on one or two coats of varnish.
I have rollered on gloss paint before, but get a better finish with method above as you can sand the emulsion extremely flat.