How to talk about cooking a dish with multiple items
Edit:
Clarification by the OP

I place all the vegetables in a pot with rice and cook them. I think 加 would indicate I add them in after cooking the rice

In this case, 煮饭 means 'cook rice', 加 would mean you add them into the raw rice when you cook them
The sentence would be

我煮饭時会把番茄，西兰花，胡萝卜和辣椒加在米中一起煮 (when I cook rice, I would add tomato, broccoli, carrot, and pepper into the raw rice)

or

我会把番茄，西兰花，胡萝卜和辣椒加在煮好的饭中一起再煮 (I would add tomatoes, broccoli, carrots, and peppers into the cooked rice and cook them together

Previous answer before the Clarification:
'煮饭' means 'to cook' in general (饭 here refer to 'meal' ).
Note:
煮饭 (to cook) sounds Cantonese. In Mandarin, the common word for 'to    cook' is 做飯 (cook meal) or 做菜(cook dish),
and 煮饭 would just mean 'cook rice' The reason I presume by 煮饭 you meant 'to cook' because it is wired to add those things in streamed rice
If you meant you are using these ingredients to cook a dish. The correct verb phrase is:
我用番茄，西兰花，胡萝卜和辣椒(来煮这道菜) = I use tomatoes, broccoli, carrots, and peppers (to cook this dish)
or
(这道菜的材料是)番茄，西兰花，胡萝卜和辣椒 = (the ingredients of this dish are) tomatoes, broccoli, carrots, and peppers

我跟西兰花，胡萝卜，辣椒，番茄煮饭

It means &quot;我 (and) 胡萝卜，辣椒，番茄煮饭 cook together&quot; (胡萝卜，辣椒，番茄 can't cook). It is nonsensical
To be more precise.

我會用番茄，西兰花，胡萝卜和辣椒来煮这道菜 (I will cook this dish with tomatoes, broccoli, carrots and peppers)

or

我用了番茄，西兰花，胡萝卜和辣椒来煮这道菜 (I used tomatoes, broccoli, carrots, and peppers to cook this dish)