Sure. Let's start by quantifying the nutritional content of one large (50 gram) egg.
- Protein: 6.3 grams
- Cholesterol: 186 mg
- Vitamin D3 (cholecalciferol): 44 IU
- Iron: 0.6 mg
And we want to get all this within an energy budget of 77 kcal.
Let's start with macronutrients because those are bounded by hard limits on energy. We know that protein provides 4 kcal per gram, so one egg provides 25 kcal energy from protein, or about 33%. To meet the protein goal we'll need to identify a food that meets or exceeds 33% energy from protein. Most whole plant foods are lower than that, but I happen to know that nutritional yeast provides 50% energy from protein, we can use 12 grams of nutritional yeast to provide 6.4 grams of protein in 45 kcal.
I'll skip right past cholesterol because there are no vegan foods that provide it.
Vitamin D3 (cholecalciferol, aka "the sunshine vitamin") is not found in most plants, although it is found in lichens! Most people are unable or unwilling to eat lichen however, so vitamin D3 can be obtained from a supplement. A single tablet provides 1000 IU, so one tablet provides as much D3 as 22 large eggs. Or if you'd rather not purchase a supplement, you can get vitamin D3 by exposing your skin to sunshine. Going outside in the midday sun in summertime in light clothing will produce about 1000 IU per minute, so you would need just 3 seconds of sun exposure to get the same amount of vitamin D3 as from one large egg. If you're okay with Vitamin D2 instead of D3 (good, but maybe not as good) then you can get it from mushrooms, although the concentration varies too much for me to provide a quantity recommendation. And if you're okay getting your D2 from fortified foods, then you can get 44 IU from 105 grams of unsweetened almond milk in just 13 kcal.
The desired amount of iron is already provided by the quantity of nutritional yeast mentioned above. Other high sources of iron are spinach (make sure it's cooked!!) and other leafy greens. Legumes (such as lentils) are also a source of iron. But we don't need those for answering this question.
That leaves us with a final answer:
- 12 grams (1.5 tbsp) nutritional yeast - 45 kcal
- 105 grams unsweetened, fortified almond milk - 13 kcal
This combination of foods provides the nutrients you're looking for, and does it with 25% less calories (58 kcal) than chicken eggs (77 kcal).
Here are some nutritional differences that you did not mention as priorities:
- The nooch/milk combo is much richer in B vitamins (like 100x more)
- Only fortified nutritional yeast provides vitamin B12. If fortified, it provides B12 in excess of what an egg provides.
- The vegan combo provides more of your daily folate.
- The egg provides more Vitamin A, and it does so in a different form (as retinol)
- The vegan combo provides more Vitamin E (from the almond milk)
- Both eggs and nutritional yeast are a complete protein
- The eggs provide saturated fat, while the vegan has none
- The vegan combo provides less fat overall
- The almond milk provides much more calcium than the egg
- The vegan combo provides more potassium
- The nutritional yeast provides much more zinc
I'll leave it as an exercise to the reader to determine the most palatable way to eat 1.5 tbsp of nooch and a half cup of plant-based milk.
TL;DR Yes, there is at least one combination of vegan foods that mirrors (or exceeds) the nutritional value of an egg.