Debbie, majority of India's population is comprised of Hindu's they don't eat beef so majority of the authentic curry recipes you will find are made with lamb. This does not mean you cannot substitute beef for it.
Also traditional Indian meat curries never have carrots and peas added to them, it's not that it's not a good addition but it's not authentic. This is an edit that the west has made to the curries.
Here is a recipe that you can use.
3 pounds of beef ( I would use boneless and a good quality cut) - Get it cut into medium size cubes
1 large onion thinly sliced
1 large tomatoes finely chopped or a better option is buying the smallest can of tomato sauce (works better than fresh)
4 cloves of garlic minced
1/2 stick of fresh ginger minced
2 tbsp of plain yogurt
Oil - 3 tbsps
2 glasses of water
1 tbsp of freshly roasted and ground cumin
1 tbsp of freshly roasted and ground corrainder
2 tsp of cayanne or red chili powder
2 tsp of garam masala - You can make your own basic version by combining 2 sticks of cinnamon, 3 cloves, 3 cardamom pods and a handful of black peppercorns. It makes a better substitute than what you buy in a ready made package because it's freshly made
salt to taste
Cilantro and Sliced boiled eggs for garnish
In a saute pan add the oil. Saute the onions until they are golden brown and almost crisp. Next add the ginger, garlic and saute them for a minute to get rid of the raw taste. Now add the tomato sauce or fresh tomatoes and saute it for several minutes. Add all the dry spices and the yogurt, meat and water and let it all cook until the meat is tender.
I normally use a pressure cooker but you can cook it in the same pan or in the oven. The curry should be ready in an hour and a half.
Serve in a nice shallow bowl garnished with freshly chopped cilantro and sliced eggs with naan and some white rice. I also like to make a simple salad with sliced onions, cucumbers, tomatoes, freshly chopped cilantro, mint, lime juice, salt and black pepper that goes well as a side.