Boiling is no-no cos the water-soluble vitamins end up in the water.
Unless you are cooking vegetable stock and using the stock to cook porridge/rice or let baby drink as soup.
Usually, I steam vegetables for 15-20 minutes using electric steamer, with timer, so it'd switch off. Remove promptly so it won't overcook.
For harder items like carrots / potatoes, cut into small cubes and steam for about 20 minutes until soft. As long as can poke a fork easily into the cube is fine.
For spinach, 15 minutes should be enough time. Young babies may be affected by nitrates in spinach and carrots, so I usually get organic ones and dont't add the steam water into baby's food. For toddler, should be fine.