If you eat carbohydrate which a sandwich will be, you should inject insulin to cover it, really.
Depending on your insulin to carbohydrate ratio and how high or low your blood glucose is before you start eating, you should be able to determine an insulin injection.
If you haven't learned to count carbohydrates yet, I would visit
http://www.bdec-e-learning.com/ over the weekend to get familiar with the concept.
NovoRapid for me has a peak around 1 hour after a meal, works well for 2 hours and then fades slowly for the following 3 hours.
If you have dinner within 2 hours of the sandwich, you may need only half the dose then for your dinner.
Personally, I would not eat a sandwich without insulin - have you tried checking your blood glucose before dinner if you don't have the insulin with the sandwich?
Insulin is not a static dose, really - it is dependant on how much sugar (sugar, fruit, starch etc) you eat, which will then later need to be removed from your blood stream.
You could probably more or less circumvent the sandwich problem by substituting the sandwich for something that contains very little carbohydrate - like a salad with vegetables and chicken cubes or something like that.
As a general rule, if you eat 10g of carbohydrate, you need 1 unit of insulin. Probably a bit more insulin in the morning, probably a bit less in the evening, and you may be different too. But having a sandwich first and then 'also' dinner, you will probably need something closer to 2 doses of insulin rather than a real split one - of course unless you have so far been running high before dinner due to said sandwich that you have gotten used to a rather large correction dose.
Hope this makes sense?
For me that would mean I take 2 units, maybe 3 at tea time with the sandwich (depending on carbohydrate content). Then at dinner say around 19 or so, I would take 2-4 more units depending on my blood sugar and the carbohydrates in my dinner. If this time is less than 2 hours after 'tea', I would have about 1 unit of insulin from the previous injection still working in my blood stream and I would be conservative about the next injection. If it is more than 3 hours, I would be more aggressive and take the extra unit. This is only my personal ratios for a relatively normal meal size and composition - it may not be the same for you, but the illustration should work. I generally lean towards Low-Carb, so at this present point in time, I try to avoid most carbohydrates and thus my insulin need is less than above - but in the example you describe, this was what I would do.