I don't find that this is ever a problem for me. YMMV, but I'd suggest eating calorie-dense foods such as nuts, beans, grains, and fatty foods.

This LiveStrong article has a sample meal plan:

A meal plan that provides over 3,000 calories begins with 1 cup of cooked quinoa topped with1/4 cup raisins, 1 oz. toasted almonds, 1 tbsp. honey and 1 cup hemp milk. For lunch, have 2 cups of whole wheat pasta tossed with 1 tbsp. olive oil, 1 cup white beans and sautéed kale. Dinner might include 6 oz. of firm tofu stir fried with broccoli, soy sauce, 1 oz. cashews and served over 1 cup brown rice. Snack on a peanut butter and jelly sandwich, made with whole grain bread, 2 tbsp. peanut butter and all-fruit spread; ½ cup of granola with soy milk and a smoothie made by blending a frozen banana with mangos, flaxseed meal, almond butter and coconut water.

I don't have this problem with most any food so I'm not sure what exactly might cause it, but if you find that you have this problem with vegetarian food and not with meat, I'd try heavy stuff like cheese omelets, preferred unmeats with nice sauces on them, maybe bean stew.

If you're having issues with your hunger response, it's almost certainly because you've simply eliminated meat from the meal, without replacing it with something nutritionally equal. Your hunger response is mediated by a number of food chemicals, which you've like never had to notice before because meat provides the appropriate ones automatically,

Solving it is easy - just eat protein (nuts, beans, etc) and fat (nuts, oil, peanut butter, etc.). That'll hit you with the right stuff to replace what you're losing with meat, and keep your stomach's brain happy because it's receiving the right chemicals.

People too often think vegetarianism is just a light salad at every meal. >_<

It could be that the vegetarian stuff you are eating doesn't have much protein in it. Or that the protein source doesn't have all the amino acids. There is certainly vegetarian stuff that does have these things, it just takes more knowledge and meal design that for meat diets.

Protein powder can also be helpful for vegetarians (and everyone). I recommend pea protein powder.